What is the LCM of 15 and 1000 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 15 and 1000, is defined as the smallest positive integer that is divisible by both. It is written as LCM(15, 1000).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 15 and 1000 is 3000, where 15 and 1000 are less than 3000.
LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
The LCM of two or more prime numbers is exactly equal to their product.
LCM is associative which means LCM(15, 1000) = LCM(1000, 15).
LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 15 and 1000 by Listing Method

Find some first multiples of 15 and 1000.
Find the least common multiple, and read off the answer!

Example: Find lcm of 15 and 1000 by Listing Method

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, 765, 780, 795, 810, 825, 840, 855, 870, 885, 900, 915, 930, 945, 960, 975, 990, 1005, 1020, 1035, 1050, 1065, 1080, 1095, 1110, 1125, 1140, 1155, 1170, 1185, 1200, 1215, 1230, 1245, 1260, 1275, 1290, 1305, 1320, 1335, 1350, 1365, 1380, 1395, 1410, 1425, 1440, 1455, 1470, 1485, 1500, 1515, 1530, 1545, 1560, 1575, 1590, 1605, 1620, 1635, 1650, 1665, 1680, 1695, 1710, 1725, 1740, 1755, 1770, 1785, 1800, 1815, 1830, 1845, 1860, 1875, 1890, 1905, 1920, 1935, 1950, 1965, 1980, 1995, 2010, 2025, 2040, 2055, 2070, 2085, 2100, 2115, 2130, 2145, 2160, 2175, 2190, 2205, 2220, 2235, 2250, 2265, 2280, 2295, 2310, 2325, 2340, 2355, 2370, 2385, 2400, 2415, 2430, 2445, 2460, 2475, 2490, 2505, 2520, 2535, 2550, 2565, 2580, 2595, 2610, 2625, 2640, 2655, 2670, 2685, 2700, 2715, 2730, 2745, 2760, 2775, 2790, 2805, 2820, 2835, 2850, 2865, 2880, 2895, 2910, 2925, 2940, 2955, 2970, 2985, 3000, 3015, 3030, 3045, 3060, 3075, 3090, 3105, 3120, 3135, 3150, 3165, 3180, 3195, 3210, 3225, 3240, 3255, 3270, 3285, 3300, 3315, 3330, 3345, 3360, 3375, 3390, 3405, 3420, 3435, 3450, 3465, 3480, 3495, 3510, 3525, 3540, 3555, 3570, 3585, 3600, 3615, 3630, 3645, 3660, 3675, 3690, 3705, 3720, 3735, 3750, 3765, 3780, 3795, 3810, 3825, 3840, 3855, 3870, 3885, 3900, 3915, 3930, 3945, 3960, 3975, 3990, 4005, 4020, 4035, 4050, 4065, 4080, 4095, 4110, 4125, 4140, 4155, 4170, 4185, 4200, 4215, 4230, 4245, 4260, 4275, 4290, 4305, 4320, 4335, 4350, 4365, 4380, 4395, 4410, 4425, 4440, 4455, 4470, 4485, 4500, 4515, 4530, 4545, 4560, 4575, 4590, 4605, 4620, 4635, 4650, 4665, 4680, 4695, 4710, 4725, 4740, 4755, 4770, 4785, 4800, 4815, 4830, 4845, 4860, 4875, 4890, 4905, 4920, 4935, 4950, 4965, 4980, 4995, 5010, 5025, 5040, 5055, 5070, 5085, 5100, 5115, 5130, 5145, 5160, 5175, 5190, 5205, 5220, 5235, 5250, 5265, 5280, 5295, 5310, 5325, 5340, 5355, 5370, 5385, 5400, 5415, 5430, 5445, 5460, 5475, 5490, 5505, 5520, 5535, 5550, 5565, 5580, 5595, 5610, 5625, 5640, 5655, 5670, 5685, 5700, 5715, 5730, 5745, 5760, 5775, 5790, 5805, 5820, 5835, 5850, 5865, 5880, 5895, 5910, 5925, 5940, 5955, 5970, 5985, 6000, 6015, 6030, 6045, 6060, 6075, 6090, 6105, 6120, 6135, 6150, 6165, 6180, 6195, 6210, 6225, 6240, 6255, 6270, 6285, 6300, 6315, 6330, 6345, 6360, 6375, 6390, 6405, 6420, 6435, 6450, 6465, 6480, 6495, 6510, 6525, 6540, 6555, 6570, 6585, 6600, 6615, 6630, 6645, 6660, 6675, 6690, 6705, 6720, 6735, 6750, 6765, 6780, 6795, 6810, 6825, 6840, 6855, 6870, 6885, 6900, 6915, 6930, 6945, 6960, 6975, 6990, 7005, 7020, 7035, 7050, 7065, 7080, 7095, 7110, 7125, 7140, 7155, 7170, 7185, 7200, 7215, 7230, 7245, 7260, 7275, 7290, 7305, 7320, 7335, 7350, 7365, 7380, 7395, 7410, 7425, 7440, 7455, 7470, 7485, 7500, 7515, 7530, 7545, 7560, 7575, 7590, 7605, 7620, 7635, 7650, 7665, 7680, 7695, 7710, 7725, 7740, 7755, 7770, 7785, 7800, 7815, 7830, 7845, 7860, 7875, 7890, 7905, 7920, 7935, 7950, 7965, 7980, 7995, 8010, 8025, 8040, 8055, 8070, 8085, 8100, 8115, 8130, 8145, 8160, 8175, 8190, 8205, 8220, 8235, 8250, 8265, 8280, 8295, 8310, 8325, 8340, 8355, 8370, 8385, 8400, 8415, 8430, 8445, 8460, 8475, 8490, 8505, 8520, 8535, 8550, 8565, 8580, 8595, 8610, 8625, 8640, 8655, 8670, 8685, 8700, 8715, 8730, 8745, 8760, 8775, 8790, 8805, 8820, 8835, 8850, 8865, 8880, 8895, 8910, 8925, 8940, 8955, 8970, 8985, 9000, 9015, 9030, 9045, 9060, 9075, 9090, 9105, 9120, 9135, 9150, 9165, 9180, 9195, 9210, 9225, 9240, 9255, 9270, 9285, 9300, 9315, 9330, 9345, 9360, 9375, 9390, 9405, 9420, 9435, 9450, 9465, 9480, 9495, 9510, 9525, 9540, 9555, 9570, 9585, 9600, 9615, 9630, 9645, 9660, 9675, 9690, 9705, 9720, 9735, 9750, 9765, 9780, 9795, 9810, 9825, 9840, 9855, 9870, 9885, 9900, 9915, 9930, 9945, 9960, 9975, 9990, 10005, 10020, 10035, 10050, 10065, 10080, 10095, 10110, 10125, 10140, 10155, 10170, 10185, 10200, 10215, 10230, 10245, 10260, 10275, 10290, 10305, 10320, 10335, 10350, 10365, 10380, 10395, 10410, 10425, 10440, 10455, 10470, 10485, 10500, 10515, 10530, 10545, 10560, 10575, 10590, 10605, 10620, 10635, 10650, 10665, 10680, 10695, 10710, 10725, 10740, 10755, 10770, 10785, 10800, 10815, 10830, 10845, 10860, 10875, 10890, 10905, 10920, 10935, 10950, 10965, 10980, 10995, 11010, 11025, 11040, 11055, 11070, 11085, 11100, 11115, 11130, 11145, 11160, 11175, 11190, 11205, 11220, 11235, 11250, 11265, 11280, 11295, 11310, 11325, 11340, 11355, 11370, 11385, 11400, 11415, 11430, 11445, 11460, 11475, 11490, 11505, 11520, 11535, 11550, 11565, 11580, 11595, 11610, 11625, 11640, 11655, 11670, 11685, 11700, 11715, 11730, 11745, 11760, 11775, 11790, 11805, 11820, 11835, 11850, 11865, 11880, 11895, 11910, 11925, 11940, 11955, 11970, 11985, 12000, 12015, 12030, 12045, 12060, 12075, 12090, 12105, 12120, 12135, 12150, 12165, 12180, 12195, 12210, 12225, 12240, 12255, 12270, 12285, 12300, 12315, 12330, 12345, 12360, 12375, 12390, 12405, 12420, 12435, 12450, 12465, 12480, 12495, 12510, 12525, 12540, 12555, 12570, 12585, 12600, 12615, 12630, 12645, 12660, 12675, 12690, 12705, 12720, 12735, 12750, 12765, 12780, 12795, 12810, 12825, 12840, 12855, 12870, 12885, 12900, 12915, 12930, 12945, 12960, 12975, 12990, 13005, 13020, 13035, 13050, 13065, 13080, 13095, 13110, 13125, 13140, 13155, 13170, 13185, 13200, 13215, 13230, 13245, 13260, 13275, 13290, 13305, 13320, 13335, 13350, 13365, 13380, 13395, 13410, 13425, 13440, 13455, 13470, 13485, 13500, 13515, 13530, 13545, 13560, 13575, 13590, 13605, 13620, 13635, 13650, 13665, 13680, 13695, 13710, 13725, 13740, 13755, 13770, 13785, 13800, 13815, 13830, 13845, 13860, 13875, 13890, 13905, 13920, 13935, 13950, 13965, 13980, 13995, 14010, 14025, 14040, 14055, 14070, 14085, 14100, 14115, 14130, 14145, 14160, 14175, 14190, 14205, 14220, 14235, 14250, 14265, 14280, 14295, 14310, 14325, 14340, 14355, 14370, 14385, 14400, 14415, 14430, 14445, 14460, 14475, 14490, 14505, 14520, 14535, 14550, 14565, 14580, 14595, 14610, 14625, 14640, 14655, 14670, 14685, 14700, 14715, 14730, 14745, 14760, 14775, 14790, 14805, 14820, 14835, 14850, 14865, 14880, 14895, 14910, 14925, 14940, 14955, 14970, 14985, 15000
Multiples of 1000: 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000

Hence, LCM of 15 and 1000 is 3000.

Steps to find LCM of 15 and 1000 by Common Division Method

Find all the prime numbers that would divide 15 and 1000 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 15 and 1000 by Common Division Method

2	15 1000
2	15 500
2	15 250
3	15 125
5	5 125
5	1 25
5	1 5
	1 1

Hence, LCM of 15 and 1000 is 2 x 2 x 2 x 3 x 5 x 5 x 5 = 3000.

Steps to find lcm of 15 and 1000 by Formula

The formula for LCM is LCM (15, 1000) = (15 x 1000) / GCF (15, 1000)
Apply the formula, and read off the answer!

Example: Find lcm of 15 and 1000 by Formula

GCF of 15 and 1000 = 5
LCM of 15 and 1000 = (15 x 1000) / 5
=> 15000 / 5

Hence, LCM of 15 and 1000 is 3000.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 15 and 1000 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 15 and 1000 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 15 and 1000.
So, LCM of 15 and 1000 is 3000.

Boxes that are 15 inches tall are being pilled next to boxes that are 1000 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 15 and 1000.
So, LCM of 15 and 1000 is 3000.

Sammy's company prints 15 textbooks at a time. Daniel's company prints textbooks in sets of 1000 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 15 and 1000.
So, LCM of 15 and 1000 is 3000.

Ariel exercises every 15 days and Rubel every 1000 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 15 and 1000 is 3000.

Find the LCM of 15 and 1000 using GCF method.

Greatest common factor or gcf of 15 and 1000 is GCF(15, 1000) x LCM(15, 1000) = (15 x 1000) / GCF(15, 1000) = 3000.

Find the least common multiple of 15 and 1000.

Least common multiple of 15 and 1000 is 3000.

Find the least number which is exactly divisible by 15 and 1000.

Least number which is exactly divisible by 15 and 1000 is 3000.

What is LCM of 15 and 1000?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 15 and 1000 by Listing Method

Example: Find lcm of 15 and 1000 by Listing Method

Steps to find LCM of 15 and 1000 by Common Division Method

Example: Find lcm of 15 and 1000 by Common Division Method

Steps to find lcm of 15 and 1000 by Formula

Example: Find lcm of 15 and 1000 by Formula

Examples

What is LCM of 15 and 1000?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 15 and 1000 by Listing Method

Example: Find lcm of 15 and 1000 by Listing Method

Steps to find LCM of 15 and 1000 by Common Division Method

Example: Find lcm of 15 and 1000 by Common Division Method

Steps to find lcm of 15 and 1000 by Formula

Example: Find lcm of 15 and 1000 by Formula

Examples

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