What is the LCM of 12 and 2000 - Find out answer step by step

How do we define LCM?

LCM, abbreviation for least common multiple, is defined as the smallest number that is the product of two or more numbers 12 and 2000

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 12 and 2000 is 6000, where 12 and 2000 are less than 6000.
LCM is associative which means LCM(12, 2000) = LCM(2000, 12).
LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
The LCM of two or more prime numbers is their product.

Steps to find lcm of 12 and 2000 by Listing Method

Find some first multiples of 12 and 2000.
Find the least common multiple, and read off the answer!

Example: Find lcm of 12 and 2000 by Listing Method

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636, 648, 660, 672, 684, 696, 708, 720, 732, 744, 756, 768, 780, 792, 804, 816, 828, 840, 852, 864, 876, 888, 900, 912, 924, 936, 948, 960, 972, 984, 996, 1008, 1020, 1032, 1044, 1056, 1068, 1080, 1092, 1104, 1116, 1128, 1140, 1152, 1164, 1176, 1188, 1200, 1212, 1224, 1236, 1248, 1260, 1272, 1284, 1296, 1308, 1320, 1332, 1344, 1356, 1368, 1380, 1392, 1404, 1416, 1428, 1440, 1452, 1464, 1476, 1488, 1500, 1512, 1524, 1536, 1548, 1560, 1572, 1584, 1596, 1608, 1620, 1632, 1644, 1656, 1668, 1680, 1692, 1704, 1716, 1728, 1740, 1752, 1764, 1776, 1788, 1800, 1812, 1824, 1836, 1848, 1860, 1872, 1884, 1896, 1908, 1920, 1932, 1944, 1956, 1968, 1980, 1992, 2004, 2016, 2028, 2040, 2052, 2064, 2076, 2088, 2100, 2112, 2124, 2136, 2148, 2160, 2172, 2184, 2196, 2208, 2220, 2232, 2244, 2256, 2268, 2280, 2292, 2304, 2316, 2328, 2340, 2352, 2364, 2376, 2388, 2400, 2412, 2424, 2436, 2448, 2460, 2472, 2484, 2496, 2508, 2520, 2532, 2544, 2556, 2568, 2580, 2592, 2604, 2616, 2628, 2640, 2652, 2664, 2676, 2688, 2700, 2712, 2724, 2736, 2748, 2760, 2772, 2784, 2796, 2808, 2820, 2832, 2844, 2856, 2868, 2880, 2892, 2904, 2916, 2928, 2940, 2952, 2964, 2976, 2988, 3000, 3012, 3024, 3036, 3048, 3060, 3072, 3084, 3096, 3108, 3120, 3132, 3144, 3156, 3168, 3180, 3192, 3204, 3216, 3228, 3240, 3252, 3264, 3276, 3288, 3300, 3312, 3324, 3336, 3348, 3360, 3372, 3384, 3396, 3408, 3420, 3432, 3444, 3456, 3468, 3480, 3492, 3504, 3516, 3528, 3540, 3552, 3564, 3576, 3588, 3600, 3612, 3624, 3636, 3648, 3660, 3672, 3684, 3696, 3708, 3720, 3732, 3744, 3756, 3768, 3780, 3792, 3804, 3816, 3828, 3840, 3852, 3864, 3876, 3888, 3900, 3912, 3924, 3936, 3948, 3960, 3972, 3984, 3996, 4008, 4020, 4032, 4044, 4056, 4068, 4080, 4092, 4104, 4116, 4128, 4140, 4152, 4164, 4176, 4188, 4200, 4212, 4224, 4236, 4248, 4260, 4272, 4284, 4296, 4308, 4320, 4332, 4344, 4356, 4368, 4380, 4392, 4404, 4416, 4428, 4440, 4452, 4464, 4476, 4488, 4500, 4512, 4524, 4536, 4548, 4560, 4572, 4584, 4596, 4608, 4620, 4632, 4644, 4656, 4668, 4680, 4692, 4704, 4716, 4728, 4740, 4752, 4764, 4776, 4788, 4800, 4812, 4824, 4836, 4848, 4860, 4872, 4884, 4896, 4908, 4920, 4932, 4944, 4956, 4968, 4980, 4992, 5004, 5016, 5028, 5040, 5052, 5064, 5076, 5088, 5100, 5112, 5124, 5136, 5148, 5160, 5172, 5184, 5196, 5208, 5220, 5232, 5244, 5256, 5268, 5280, 5292, 5304, 5316, 5328, 5340, 5352, 5364, 5376, 5388, 5400, 5412, 5424, 5436, 5448, 5460, 5472, 5484, 5496, 5508, 5520, 5532, 5544, 5556, 5568, 5580, 5592, 5604, 5616, 5628, 5640, 5652, 5664, 5676, 5688, 5700, 5712, 5724, 5736, 5748, 5760, 5772, 5784, 5796, 5808, 5820, 5832, 5844, 5856, 5868, 5880, 5892, 5904, 5916, 5928, 5940, 5952, 5964, 5976, 5988, 6000, 6012, 6024, 6036, 6048, 6060, 6072, 6084, 6096, 6108, 6120, 6132, 6144, 6156, 6168, 6180, 6192, 6204, 6216, 6228, 6240, 6252, 6264, 6276, 6288, 6300, 6312, 6324, 6336, 6348, 6360, 6372, 6384, 6396, 6408, 6420, 6432, 6444, 6456, 6468, 6480, 6492, 6504, 6516, 6528, 6540, 6552, 6564, 6576, 6588, 6600, 6612, 6624, 6636, 6648, 6660, 6672, 6684, 6696, 6708, 6720, 6732, 6744, 6756, 6768, 6780, 6792, 6804, 6816, 6828, 6840, 6852, 6864, 6876, 6888, 6900, 6912, 6924, 6936, 6948, 6960, 6972, 6984, 6996, 7008, 7020, 7032, 7044, 7056, 7068, 7080, 7092, 7104, 7116, 7128, 7140, 7152, 7164, 7176, 7188, 7200, 7212, 7224, 7236, 7248, 7260, 7272, 7284, 7296, 7308, 7320, 7332, 7344, 7356, 7368, 7380, 7392, 7404, 7416, 7428, 7440, 7452, 7464, 7476, 7488, 7500, 7512, 7524, 7536, 7548, 7560, 7572, 7584, 7596, 7608, 7620, 7632, 7644, 7656, 7668, 7680, 7692, 7704, 7716, 7728, 7740, 7752, 7764, 7776, 7788, 7800, 7812, 7824, 7836, 7848, 7860, 7872, 7884, 7896, 7908, 7920, 7932, 7944, 7956, 7968, 7980, 7992, 8004, 8016, 8028, 8040, 8052, 8064, 8076, 8088, 8100, 8112, 8124, 8136, 8148, 8160, 8172, 8184, 8196, 8208, 8220, 8232, 8244, 8256, 8268, 8280, 8292, 8304, 8316, 8328, 8340, 8352, 8364, 8376, 8388, 8400, 8412, 8424, 8436, 8448, 8460, 8472, 8484, 8496, 8508, 8520, 8532, 8544, 8556, 8568, 8580, 8592, 8604, 8616, 8628, 8640, 8652, 8664, 8676, 8688, 8700, 8712, 8724, 8736, 8748, 8760, 8772, 8784, 8796, 8808, 8820, 8832, 8844, 8856, 8868, 8880, 8892, 8904, 8916, 8928, 8940, 8952, 8964, 8976, 8988, 9000, 9012, 9024, 9036, 9048, 9060, 9072, 9084, 9096, 9108, 9120, 9132, 9144, 9156, 9168, 9180, 9192, 9204, 9216, 9228, 9240, 9252, 9264, 9276, 9288, 9300, 9312, 9324, 9336, 9348, 9360, 9372, 9384, 9396, 9408, 9420, 9432, 9444, 9456, 9468, 9480, 9492, 9504, 9516, 9528, 9540, 9552, 9564, 9576, 9588, 9600, 9612, 9624, 9636, 9648, 9660, 9672, 9684, 9696, 9708, 9720, 9732, 9744, 9756, 9768, 9780, 9792, 9804, 9816, 9828, 9840, 9852, 9864, 9876, 9888, 9900, 9912, 9924, 9936, 9948, 9960, 9972, 9984, 9996, 10008, 10020, 10032, 10044, 10056, 10068, 10080, 10092, 10104, 10116, 10128, 10140, 10152, 10164, 10176, 10188, 10200, 10212, 10224, 10236, 10248, 10260, 10272, 10284, 10296, 10308, 10320, 10332, 10344, 10356, 10368, 10380, 10392, 10404, 10416, 10428, 10440, 10452, 10464, 10476, 10488, 10500, 10512, 10524, 10536, 10548, 10560, 10572, 10584, 10596, 10608, 10620, 10632, 10644, 10656, 10668, 10680, 10692, 10704, 10716, 10728, 10740, 10752, 10764, 10776, 10788, 10800, 10812, 10824, 10836, 10848, 10860, 10872, 10884, 10896, 10908, 10920, 10932, 10944, 10956, 10968, 10980, 10992, 11004, 11016, 11028, 11040, 11052, 11064, 11076, 11088, 11100, 11112, 11124, 11136, 11148, 11160, 11172, 11184, 11196, 11208, 11220, 11232, 11244, 11256, 11268, 11280, 11292, 11304, 11316, 11328, 11340, 11352, 11364, 11376, 11388, 11400, 11412, 11424, 11436, 11448, 11460, 11472, 11484, 11496, 11508, 11520, 11532, 11544, 11556, 11568, 11580, 11592, 11604, 11616, 11628, 11640, 11652, 11664, 11676, 11688, 11700, 11712, 11724, 11736, 11748, 11760, 11772, 11784, 11796, 11808, 11820, 11832, 11844, 11856, 11868, 11880, 11892, 11904, 11916, 11928, 11940, 11952, 11964, 11976, 11988, 12000, 12012, 12024, 12036, 12048, 12060, 12072, 12084, 12096, 12108, 12120, 12132, 12144, 12156, 12168, 12180, 12192, 12204, 12216, 12228, 12240, 12252, 12264, 12276, 12288, 12300, 12312, 12324, 12336, 12348, 12360, 12372, 12384, 12396, 12408, 12420, 12432, 12444, 12456, 12468, 12480, 12492, 12504, 12516, 12528, 12540, 12552, 12564, 12576, 12588, 12600, 12612, 12624, 12636, 12648, 12660, 12672, 12684, 12696, 12708, 12720, 12732, 12744, 12756, 12768, 12780, 12792, 12804, 12816, 12828, 12840, 12852, 12864, 12876, 12888, 12900, 12912, 12924, 12936, 12948, 12960, 12972, 12984, 12996, 13008, 13020, 13032, 13044, 13056, 13068, 13080, 13092, 13104, 13116, 13128, 13140, 13152, 13164, 13176, 13188, 13200, 13212, 13224, 13236, 13248, 13260, 13272, 13284, 13296, 13308, 13320, 13332, 13344, 13356, 13368, 13380, 13392, 13404, 13416, 13428, 13440, 13452, 13464, 13476, 13488, 13500, 13512, 13524, 13536, 13548, 13560, 13572, 13584, 13596, 13608, 13620, 13632, 13644, 13656, 13668, 13680, 13692, 13704, 13716, 13728, 13740, 13752, 13764, 13776, 13788, 13800, 13812, 13824, 13836, 13848, 13860, 13872, 13884, 13896, 13908, 13920, 13932, 13944, 13956, 13968, 13980, 13992, 14004, 14016, 14028, 14040, 14052, 14064, 14076, 14088, 14100, 14112, 14124, 14136, 14148, 14160, 14172, 14184, 14196, 14208, 14220, 14232, 14244, 14256, 14268, 14280, 14292, 14304, 14316, 14328, 14340, 14352, 14364, 14376, 14388, 14400, 14412, 14424, 14436, 14448, 14460, 14472, 14484, 14496, 14508, 14520, 14532, 14544, 14556, 14568, 14580, 14592, 14604, 14616, 14628, 14640, 14652, 14664, 14676, 14688, 14700, 14712, 14724, 14736, 14748, 14760, 14772, 14784, 14796, 14808, 14820, 14832, 14844, 14856, 14868, 14880, 14892, 14904, 14916, 14928, 14940, 14952, 14964, 14976, 14988, 15000, 15012, 15024, 15036, 15048, 15060, 15072, 15084, 15096, 15108, 15120, 15132, 15144, 15156, 15168, 15180, 15192, 15204, 15216, 15228, 15240, 15252, 15264, 15276, 15288, 15300, 15312, 15324, 15336, 15348, 15360, 15372, 15384, 15396, 15408, 15420, 15432, 15444, 15456, 15468, 15480, 15492, 15504, 15516, 15528, 15540, 15552, 15564, 15576, 15588, 15600, 15612, 15624, 15636, 15648, 15660, 15672, 15684, 15696, 15708, 15720, 15732, 15744, 15756, 15768, 15780, 15792, 15804, 15816, 15828, 15840, 15852, 15864, 15876, 15888, 15900, 15912, 15924, 15936, 15948, 15960, 15972, 15984, 15996, 16008, 16020, 16032, 16044, 16056, 16068, 16080, 16092, 16104, 16116, 16128, 16140, 16152, 16164, 16176, 16188, 16200, 16212, 16224, 16236, 16248, 16260, 16272, 16284, 16296, 16308, 16320, 16332, 16344, 16356, 16368, 16380, 16392, 16404, 16416, 16428, 16440, 16452, 16464, 16476, 16488, 16500, 16512, 16524, 16536, 16548, 16560, 16572, 16584, 16596, 16608, 16620, 16632, 16644, 16656, 16668, 16680, 16692, 16704, 16716, 16728, 16740, 16752, 16764, 16776, 16788, 16800, 16812, 16824, 16836, 16848, 16860, 16872, 16884, 16896, 16908, 16920, 16932, 16944, 16956, 16968, 16980, 16992, 17004, 17016, 17028, 17040, 17052, 17064, 17076, 17088, 17100, 17112, 17124, 17136, 17148, 17160, 17172, 17184, 17196, 17208, 17220, 17232, 17244, 17256, 17268, 17280, 17292, 17304, 17316, 17328, 17340, 17352, 17364, 17376, 17388, 17400, 17412, 17424, 17436, 17448, 17460, 17472, 17484, 17496, 17508, 17520, 17532, 17544, 17556, 17568, 17580, 17592, 17604, 17616, 17628, 17640, 17652, 17664, 17676, 17688, 17700, 17712, 17724, 17736, 17748, 17760, 17772, 17784, 17796, 17808, 17820, 17832, 17844, 17856, 17868, 17880, 17892, 17904, 17916, 17928, 17940, 17952, 17964, 17976, 17988, 18000, 18012, 18024, 18036, 18048, 18060, 18072, 18084, 18096, 18108, 18120, 18132, 18144, 18156, 18168, 18180, 18192, 18204, 18216, 18228, 18240, 18252, 18264, 18276, 18288, 18300, 18312, 18324, 18336, 18348, 18360, 18372, 18384, 18396, 18408, 18420, 18432, 18444, 18456, 18468, 18480, 18492, 18504, 18516, 18528, 18540, 18552, 18564, 18576, 18588, 18600, 18612, 18624, 18636, 18648, 18660, 18672, 18684, 18696, 18708, 18720, 18732, 18744, 18756, 18768, 18780, 18792, 18804, 18816, 18828, 18840, 18852, 18864, 18876, 18888, 18900, 18912, 18924, 18936, 18948, 18960, 18972, 18984, 18996, 19008, 19020, 19032, 19044, 19056, 19068, 19080, 19092, 19104, 19116, 19128, 19140, 19152, 19164, 19176, 19188, 19200, 19212, 19224, 19236, 19248, 19260, 19272, 19284, 19296, 19308, 19320, 19332, 19344, 19356, 19368, 19380, 19392, 19404, 19416, 19428, 19440, 19452, 19464, 19476, 19488, 19500, 19512, 19524, 19536, 19548, 19560, 19572, 19584, 19596, 19608, 19620, 19632, 19644, 19656, 19668, 19680, 19692, 19704, 19716, 19728, 19740, 19752, 19764, 19776, 19788, 19800, 19812, 19824, 19836, 19848, 19860, 19872, 19884, 19896, 19908, 19920, 19932, 19944, 19956, 19968, 19980, 19992, 20004, 20016, 20028, 20040, 20052, 20064, 20076, 20088, 20100, 20112, 20124, 20136, 20148, 20160, 20172, 20184, 20196, 20208, 20220, 20232, 20244, 20256, 20268, 20280, 20292, 20304, 20316, 20328, 20340, 20352, 20364, 20376, 20388, 20400, 20412, 20424, 20436, 20448, 20460, 20472, 20484, 20496, 20508, 20520, 20532, 20544, 20556, 20568, 20580, 20592, 20604, 20616, 20628, 20640, 20652, 20664, 20676, 20688, 20700, 20712, 20724, 20736, 20748, 20760, 20772, 20784, 20796, 20808, 20820, 20832, 20844, 20856, 20868, 20880, 20892, 20904, 20916, 20928, 20940, 20952, 20964, 20976, 20988, 21000, 21012, 21024, 21036, 21048, 21060, 21072, 21084, 21096, 21108, 21120, 21132, 21144, 21156, 21168, 21180, 21192, 21204, 21216, 21228, 21240, 21252, 21264, 21276, 21288, 21300, 21312, 21324, 21336, 21348, 21360, 21372, 21384, 21396, 21408, 21420, 21432, 21444, 21456, 21468, 21480, 21492, 21504, 21516, 21528, 21540, 21552, 21564, 21576, 21588, 21600, 21612, 21624, 21636, 21648, 21660, 21672, 21684, 21696, 21708, 21720, 21732, 21744, 21756, 21768, 21780, 21792, 21804, 21816, 21828, 21840, 21852, 21864, 21876, 21888, 21900, 21912, 21924, 21936, 21948, 21960, 21972, 21984, 21996, 22008, 22020, 22032, 22044, 22056, 22068, 22080, 22092, 22104, 22116, 22128, 22140, 22152, 22164, 22176, 22188, 22200, 22212, 22224, 22236, 22248, 22260, 22272, 22284, 22296, 22308, 22320, 22332, 22344, 22356, 22368, 22380, 22392, 22404, 22416, 22428, 22440, 22452, 22464, 22476, 22488, 22500, 22512, 22524, 22536, 22548, 22560, 22572, 22584, 22596, 22608, 22620, 22632, 22644, 22656, 22668, 22680, 22692, 22704, 22716, 22728, 22740, 22752, 22764, 22776, 22788, 22800, 22812, 22824, 22836, 22848, 22860, 22872, 22884, 22896, 22908, 22920, 22932, 22944, 22956, 22968, 22980, 22992, 23004, 23016, 23028, 23040, 23052, 23064, 23076, 23088, 23100, 23112, 23124, 23136, 23148, 23160, 23172, 23184, 23196, 23208, 23220, 23232, 23244, 23256, 23268, 23280, 23292, 23304, 23316, 23328, 23340, 23352, 23364, 23376, 23388, 23400, 23412, 23424, 23436, 23448, 23460, 23472, 23484, 23496, 23508, 23520, 23532, 23544, 23556, 23568, 23580, 23592, 23604, 23616, 23628, 23640, 23652, 23664, 23676, 23688, 23700, 23712, 23724, 23736, 23748, 23760, 23772, 23784, 23796, 23808, 23820, 23832, 23844, 23856, 23868, 23880, 23892, 23904, 23916, 23928, 23940, 23952, 23964, 23976, 23988, 24000
Multiples of 2000: 2000, 4000, 6000, 8000, 10000, 12000, 14000, 16000, 18000, 20000, 22000, 24000

Hence, LCM of 12 and 2000 is 6000.

Steps to find LCM of 12 and 2000 by Common Division Method

Find all the prime numbers that would divide 12 and 2000 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 12 and 2000 by Common Division Method

2	12 2000
2	6 1000
2	3 500
2	3 250
3	3 125
5	1 125
5	1 25
5	1 5
	1 1

Hence, LCM of 12 and 2000 is 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 6000.

Steps to find lcm of 12 and 2000 by Formula

The formula for LCM is LCM (12, 2000) = (12 x 2000) / GCF (12, 2000)
Apply the formula, and read off the answer!

Example: Find lcm of 12 and 2000 by Formula

GCF of 12 and 2000 = 4
LCM of 12 and 2000 = (12 x 2000) / 4
=> 24000 / 4

Hence, LCM of 12 and 2000 is 6000.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 12 and 2000 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 12 and 2000 minutes respectively to go round once. We need to find out at what time (minimum) they will run together again. For this we need to find the LCM of 12 and 2000.
So, LCM of 12 and 2000 is 6000.

A shopkeeper sells candies in packet of 12 and chocolates in packet of 2000. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 12 and 2000.
So, LCM of 12 and 2000 is 6000.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 12 and 2000 is GCF(12, 2000) * LCM(12, 2000) = (12 x 2000) / GCF(12, 2000) = 6000.

Sammy's company prints 12 textbooks at a time. Daniel's company prints textbooks in sets of 2000 at a time. According to a survey done by a committee, both companies printed the same number of textbooks last year. Find the least number of books that each company would have printed.

To find the least number of textbooks that each company could have printed we need to find the LCM of 12 and 2000.
So, LCM of 12 and 2000 is 6000.

Mary exercises every 12 days and Nikki every 2000 days. They both excercised today. How many days will it be until they excercise together again?

The problem can be solved using LCM, because we are trying to figure out the least time until they excercise together again.
So, LCM of 12 and 2000 is 6000.

Find the least common multiple of 12 and 2000.

Least common multiple of 12 and 2000 is 6000.

Find the least number which is exactly divisible by 12 and 2000.

Least number which is exactly divisible by 12 and 2000 is 6000.

What is LCM of 12 and 2000?

How to find lcm of two numbers

How do we define LCM?

Properties of LCM

Steps to find lcm of 12 and 2000 by Listing Method

Example: Find lcm of 12 and 2000 by Listing Method

Steps to find LCM of 12 and 2000 by Common Division Method

Example: Find lcm of 12 and 2000 by Common Division Method

Steps to find lcm of 12 and 2000 by Formula

Example: Find lcm of 12 and 2000 by Formula

Examples

What is LCM of 12 and 2000?

How to find lcm of two numbers

How do we define LCM?

Properties of LCM

Steps to find lcm of 12 and 2000 by Listing Method

Example: Find lcm of 12 and 2000 by Listing Method

Steps to find LCM of 12 and 2000 by Common Division Method

Example: Find lcm of 12 and 2000 by Common Division Method

Steps to find lcm of 12 and 2000 by Formula

Example: Find lcm of 12 and 2000 by Formula

Examples

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