What is LCM of 342 and 380?


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 342 and 380

Properties of LCM

  • LCM follows associative property, that means LCM(342, 380) = LCM(380, 342).
  • LCM follows commutative property, which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM follows distributive property, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 342 and 380 is 3420, where 342 and 380 are less than 3420.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 342 and 380 by Listing Method

Example: Find lcm of 342 and 380 by Listing Method

  • Multiples of 342: 342, 684, 1026, 1368, 1710, 2052, 2394, 2736, 3078, 3420, 3762, 4104, 4446, 4788, 5130, 5472, 5814, 6156, 6498, 6840, 7182, 7524, 7866, 8208, 8550, 8892, 9234, 9576, 9918, 10260, 10602, 10944, 11286, 11628, 11970, 12312, 12654, 12996, 13338, 13680, 14022, 14364, 14706, 15048, 15390, 15732, 16074, 16416, 16758, 17100, 17442, 17784, 18126, 18468, 18810, 19152, 19494, 19836, 20178, 20520, 20862, 21204, 21546, 21888, 22230, 22572, 22914, 23256, 23598, 23940, 24282, 24624, 24966, 25308, 25650, 25992, 26334, 26676, 27018, 27360, 27702, 28044, 28386, 28728, 29070, 29412, 29754, 30096, 30438, 30780, 31122, 31464, 31806, 32148, 32490, 32832, 33174, 33516, 33858, 34200, 34542, 34884, 35226, 35568, 35910, 36252, 36594, 36936, 37278, 37620, 37962, 38304, 38646, 38988, 39330, 39672, 40014, 40356, 40698, 41040, 41382, 41724, 42066, 42408, 42750, 43092, 43434, 43776, 44118, 44460, 44802, 45144, 45486, 45828, 46170, 46512, 46854, 47196, 47538, 47880, 48222, 48564, 48906, 49248, 49590, 49932, 50274, 50616, 50958, 51300, 51642, 51984, 52326, 52668, 53010, 53352, 53694, 54036, 54378, 54720, 55062, 55404, 55746, 56088, 56430, 56772, 57114, 57456, 57798, 58140, 58482, 58824, 59166, 59508, 59850, 60192, 60534, 60876, 61218, 61560, 61902, 62244, 62586, 62928, 63270, 63612, 63954, 64296, 64638, 64980, 65322, 65664, 66006, 66348, 66690, 67032, 67374, 67716, 68058, 68400, 68742, 69084, 69426, 69768, 70110, 70452, 70794, 71136, 71478, 71820, 72162, 72504, 72846, 73188, 73530, 73872, 74214, 74556, 74898, 75240, 75582, 75924, 76266, 76608, 76950, 77292, 77634, 77976, 78318, 78660, 79002, 79344, 79686, 80028, 80370, 80712, 81054, 81396, 81738, 82080, 82422, 82764, 83106, 83448, 83790, 84132, 84474, 84816, 85158, 85500, 85842, 86184, 86526, 86868, 87210, 87552, 87894, 88236, 88578, 88920, 89262, 89604, 89946, 90288, 90630, 90972, 91314, 91656, 91998, 92340, 92682, 93024, 93366, 93708, 94050, 94392, 94734, 95076, 95418, 95760, 96102, 96444, 96786, 97128, 97470, 97812, 98154, 98496, 98838, 99180, 99522, 99864, 100206, 100548, 100890, 101232, 101574, 101916, 102258, 102600, 102942, 103284, 103626, 103968, 104310, 104652, 104994, 105336, 105678, 106020, 106362, 106704, 107046, 107388, 107730, 108072, 108414, 108756, 109098, 109440, 109782, 110124, 110466, 110808, 111150, 111492, 111834, 112176, 112518, 112860, 113202, 113544, 113886, 114228, 114570, 114912, 115254, 115596, 115938, 116280, 116622, 116964, 117306, 117648, 117990, 118332, 118674, 119016, 119358, 119700, 120042, 120384, 120726, 121068, 121410, 121752, 122094, 122436, 122778, 123120, 123462, 123804, 124146, 124488, 124830, 125172, 125514, 125856, 126198, 126540, 126882, 127224, 127566, 127908, 128250, 128592, 128934, 129276, 129618, 129960
  • Multiples of 380: 380, 760, 1140, 1520, 1900, 2280, 2660, 3040, 3420, 3800, 4180, 4560, 4940, 5320, 5700, 6080, 6460, 6840, 7220, 7600, 7980, 8360, 8740, 9120, 9500, 9880, 10260, 10640, 11020, 11400, 11780, 12160, 12540, 12920, 13300, 13680, 14060, 14440, 14820, 15200, 15580, 15960, 16340, 16720, 17100, 17480, 17860, 18240, 18620, 19000, 19380, 19760, 20140, 20520, 20900, 21280, 21660, 22040, 22420, 22800, 23180, 23560, 23940, 24320, 24700, 25080, 25460, 25840, 26220, 26600, 26980, 27360, 27740, 28120, 28500, 28880, 29260, 29640, 30020, 30400, 30780, 31160, 31540, 31920, 32300, 32680, 33060, 33440, 33820, 34200, 34580, 34960, 35340, 35720, 36100, 36480, 36860, 37240, 37620, 38000, 38380, 38760, 39140, 39520, 39900, 40280, 40660, 41040, 41420, 41800, 42180, 42560, 42940, 43320, 43700, 44080, 44460, 44840, 45220, 45600, 45980, 46360, 46740, 47120, 47500, 47880, 48260, 48640, 49020, 49400, 49780, 50160, 50540, 50920, 51300, 51680, 52060, 52440, 52820, 53200, 53580, 53960, 54340, 54720, 55100, 55480, 55860, 56240, 56620, 57000, 57380, 57760, 58140, 58520, 58900, 59280, 59660, 60040, 60420, 60800, 61180, 61560, 61940, 62320, 62700, 63080, 63460, 63840, 64220, 64600, 64980, 65360, 65740, 66120, 66500, 66880, 67260, 67640, 68020, 68400, 68780, 69160, 69540, 69920, 70300, 70680, 71060, 71440, 71820, 72200, 72580, 72960, 73340, 73720, 74100, 74480, 74860, 75240, 75620, 76000, 76380, 76760, 77140, 77520, 77900, 78280, 78660, 79040, 79420, 79800, 80180, 80560, 80940, 81320, 81700, 82080, 82460, 82840, 83220, 83600, 83980, 84360, 84740, 85120, 85500, 85880, 86260, 86640, 87020, 87400, 87780, 88160, 88540, 88920, 89300, 89680, 90060, 90440, 90820, 91200, 91580, 91960, 92340, 92720, 93100, 93480, 93860, 94240, 94620, 95000, 95380, 95760, 96140, 96520, 96900, 97280, 97660, 98040, 98420, 98800, 99180, 99560, 99940, 100320, 100700, 101080, 101460, 101840, 102220, 102600, 102980, 103360, 103740, 104120, 104500, 104880, 105260, 105640, 106020, 106400, 106780, 107160, 107540, 107920, 108300, 108680, 109060, 109440, 109820, 110200, 110580, 110960, 111340, 111720, 112100, 112480, 112860, 113240, 113620, 114000, 114380, 114760, 115140, 115520, 115900, 116280, 116660, 117040, 117420, 117800, 118180, 118560, 118940, 119320, 119700, 120080, 120460, 120840, 121220, 121600, 121980, 122360, 122740, 123120, 123500, 123880, 124260, 124640, 125020, 125400, 125780, 126160, 126540, 126920, 127300, 127680, 128060, 128440, 128820, 129200, 129580, 129960

Hence, LCM of 342 and 380 is 3420.

Steps to find LCM of 342 and 380 by Common Division Method

Example: Find lcm of 342 and 380 by Common Division Method

2 342 380
2 171 190
3 171 95
3 57 95
5 19 95
19 19 19
1 1

Hence, LCM of 342 and 380 is 2 x 2 x 3 x 3 x 5 x 19 = 3420.

Steps to find lcm of 342 and 380 by Formula

Example: Find lcm of 342 and 380 by Formula

  • GCF of 342 and 380 = 38
  • LCM of 342 and 380 = (342 x 380) / 38
  • => 129960 / 38

Hence, LCM of 342 and 380 is 3420.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 342 and 380 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 342 and 380 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 342 and 380.
So, LCM of 342 and 380 is 3420.

A shopkeeper sells candies in packet of 342 and chocolates in packet of 380. 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 342 and 380.
So, LCM of 342 and 380 is 3420.

Both the cricket team and the rugby team had games, today. The cricket team plays every 342 days and the basketball team plays every 380 days. When will both teams have games on the same day again?

Given that the cricket team plays every 342 days and the basketball team plays every 380 days, so for finding the next time when both teams will play again we need to find the LCM of 342 and 380.
So, LCM of 342 and 380 is 3420.

Freddy saves 342 dollars every day while Nikki saves 380 dollars every day. What is the least number of days it will take each person to save the same amount of money?

To find the least number of days that would be taken to be able to save the same amount of dollars we need to find the LCM of 342 and 380.
So, LCM of 342 and 380 is 3420.

Boxes that are 342 inches tall are being pilled next to boxes that are 380 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 342 and 380.
So, LCM of 342 and 380 is 3420.

Sammy's company prints 342 textbooks at a time. Daniel's company prints textbooks in sets of 380 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 342 and 380.
So, LCM of 342 and 380 is 3420.

Ariel exercises every 342 days and Rubel every 380 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 342 and 380 is 3420.