What is the LCM of 320 and 400 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 320 and 400, is defined as the smallest positive integer that is divisible by both. It is written as LCM(320, 400).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 320 and 400 is 1600, where 320 and 400 are less than 1600.
LCM is associative which means LCM(320, 400) = LCM(400, 320).
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 320 and 400 by Listing Method

Find some first multiples of 320 and 400.
Find the least common multiple, and read off the answer!

Example: Find lcm of 320 and 400 by Listing Method

Multiples of 320: 320, 640, 960, 1280, 1600, 1920, 2240, 2560, 2880, 3200, 3520, 3840, 4160, 4480, 4800, 5120, 5440, 5760, 6080, 6400, 6720, 7040, 7360, 7680, 8000, 8320, 8640, 8960, 9280, 9600, 9920, 10240, 10560, 10880, 11200, 11520, 11840, 12160, 12480, 12800, 13120, 13440, 13760, 14080, 14400, 14720, 15040, 15360, 15680, 16000, 16320, 16640, 16960, 17280, 17600, 17920, 18240, 18560, 18880, 19200, 19520, 19840, 20160, 20480, 20800, 21120, 21440, 21760, 22080, 22400, 22720, 23040, 23360, 23680, 24000, 24320, 24640, 24960, 25280, 25600, 25920, 26240, 26560, 26880, 27200, 27520, 27840, 28160, 28480, 28800, 29120, 29440, 29760, 30080, 30400, 30720, 31040, 31360, 31680, 32000, 32320, 32640, 32960, 33280, 33600, 33920, 34240, 34560, 34880, 35200, 35520, 35840, 36160, 36480, 36800, 37120, 37440, 37760, 38080, 38400, 38720, 39040, 39360, 39680, 40000, 40320, 40640, 40960, 41280, 41600, 41920, 42240, 42560, 42880, 43200, 43520, 43840, 44160, 44480, 44800, 45120, 45440, 45760, 46080, 46400, 46720, 47040, 47360, 47680, 48000, 48320, 48640, 48960, 49280, 49600, 49920, 50240, 50560, 50880, 51200, 51520, 51840, 52160, 52480, 52800, 53120, 53440, 53760, 54080, 54400, 54720, 55040, 55360, 55680, 56000, 56320, 56640, 56960, 57280, 57600, 57920, 58240, 58560, 58880, 59200, 59520, 59840, 60160, 60480, 60800, 61120, 61440, 61760, 62080, 62400, 62720, 63040, 63360, 63680, 64000, 64320, 64640, 64960, 65280, 65600, 65920, 66240, 66560, 66880, 67200, 67520, 67840, 68160, 68480, 68800, 69120, 69440, 69760, 70080, 70400, 70720, 71040, 71360, 71680, 72000, 72320, 72640, 72960, 73280, 73600, 73920, 74240, 74560, 74880, 75200, 75520, 75840, 76160, 76480, 76800, 77120, 77440, 77760, 78080, 78400, 78720, 79040, 79360, 79680, 80000, 80320, 80640, 80960, 81280, 81600, 81920, 82240, 82560, 82880, 83200, 83520, 83840, 84160, 84480, 84800, 85120, 85440, 85760, 86080, 86400, 86720, 87040, 87360, 87680, 88000, 88320, 88640, 88960, 89280, 89600, 89920, 90240, 90560, 90880, 91200, 91520, 91840, 92160, 92480, 92800, 93120, 93440, 93760, 94080, 94400, 94720, 95040, 95360, 95680, 96000, 96320, 96640, 96960, 97280, 97600, 97920, 98240, 98560, 98880, 99200, 99520, 99840, 100160, 100480, 100800, 101120, 101440, 101760, 102080, 102400, 102720, 103040, 103360, 103680, 104000, 104320, 104640, 104960, 105280, 105600, 105920, 106240, 106560, 106880, 107200, 107520, 107840, 108160, 108480, 108800, 109120, 109440, 109760, 110080, 110400, 110720, 111040, 111360, 111680, 112000, 112320, 112640, 112960, 113280, 113600, 113920, 114240, 114560, 114880, 115200, 115520, 115840, 116160, 116480, 116800, 117120, 117440, 117760, 118080, 118400, 118720, 119040, 119360, 119680, 120000, 120320, 120640, 120960, 121280, 121600, 121920, 122240, 122560, 122880, 123200, 123520, 123840, 124160, 124480, 124800, 125120, 125440, 125760, 126080, 126400, 126720, 127040, 127360, 127680, 128000
Multiples of 400: 400, 800, 1200, 1600, 2000, 2400, 2800, 3200, 3600, 4000, 4400, 4800, 5200, 5600, 6000, 6400, 6800, 7200, 7600, 8000, 8400, 8800, 9200, 9600, 10000, 10400, 10800, 11200, 11600, 12000, 12400, 12800, 13200, 13600, 14000, 14400, 14800, 15200, 15600, 16000, 16400, 16800, 17200, 17600, 18000, 18400, 18800, 19200, 19600, 20000, 20400, 20800, 21200, 21600, 22000, 22400, 22800, 23200, 23600, 24000, 24400, 24800, 25200, 25600, 26000, 26400, 26800, 27200, 27600, 28000, 28400, 28800, 29200, 29600, 30000, 30400, 30800, 31200, 31600, 32000, 32400, 32800, 33200, 33600, 34000, 34400, 34800, 35200, 35600, 36000, 36400, 36800, 37200, 37600, 38000, 38400, 38800, 39200, 39600, 40000, 40400, 40800, 41200, 41600, 42000, 42400, 42800, 43200, 43600, 44000, 44400, 44800, 45200, 45600, 46000, 46400, 46800, 47200, 47600, 48000, 48400, 48800, 49200, 49600, 50000, 50400, 50800, 51200, 51600, 52000, 52400, 52800, 53200, 53600, 54000, 54400, 54800, 55200, 55600, 56000, 56400, 56800, 57200, 57600, 58000, 58400, 58800, 59200, 59600, 60000, 60400, 60800, 61200, 61600, 62000, 62400, 62800, 63200, 63600, 64000, 64400, 64800, 65200, 65600, 66000, 66400, 66800, 67200, 67600, 68000, 68400, 68800, 69200, 69600, 70000, 70400, 70800, 71200, 71600, 72000, 72400, 72800, 73200, 73600, 74000, 74400, 74800, 75200, 75600, 76000, 76400, 76800, 77200, 77600, 78000, 78400, 78800, 79200, 79600, 80000, 80400, 80800, 81200, 81600, 82000, 82400, 82800, 83200, 83600, 84000, 84400, 84800, 85200, 85600, 86000, 86400, 86800, 87200, 87600, 88000, 88400, 88800, 89200, 89600, 90000, 90400, 90800, 91200, 91600, 92000, 92400, 92800, 93200, 93600, 94000, 94400, 94800, 95200, 95600, 96000, 96400, 96800, 97200, 97600, 98000, 98400, 98800, 99200, 99600, 100000, 100400, 100800, 101200, 101600, 102000, 102400, 102800, 103200, 103600, 104000, 104400, 104800, 105200, 105600, 106000, 106400, 106800, 107200, 107600, 108000, 108400, 108800, 109200, 109600, 110000, 110400, 110800, 111200, 111600, 112000, 112400, 112800, 113200, 113600, 114000, 114400, 114800, 115200, 115600, 116000, 116400, 116800, 117200, 117600, 118000, 118400, 118800, 119200, 119600, 120000, 120400, 120800, 121200, 121600, 122000, 122400, 122800, 123200, 123600, 124000, 124400, 124800, 125200, 125600, 126000, 126400, 126800, 127200, 127600, 128000

Hence, LCM of 320 and 400 is 1600.

Steps to find LCM of 320 and 400 by Common Division Method

Find all the prime numbers that would divide 320 and 400 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 320 and 400 by Common Division Method

2	320 400
2	160 200
2	80 100
2	40 50
2	20 25
2	10 25
5	5 25
5	1 5
	1 1

Hence, LCM of 320 and 400 is 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 1600.

Steps to find lcm of 320 and 400 by Formula

The formula for LCM is LCM (320, 400) = (320 x 400) / GCF (320, 400)
Apply the formula, and read off the answer!

Example: Find lcm of 320 and 400 by Formula

GCF of 320 and 400 = 80
LCM of 320 and 400 = (320 x 400) / 80
=> 128000 / 80

Hence, LCM of 320 and 400 is 1600.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 320 and 400 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 320 and 400 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 320 and 400.
So, LCM of 320 and 400 is 1600.

A shopkeeper sells candies in packet of 320 and chocolates in packet of 400. 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 320 and 400.
So, LCM of 320 and 400 is 1600.

Both the cricket team and the rugby team had games, today. The cricket team plays every 320 days and the basketball team plays every 400 days. When will both teams have games on the same day again?

Given that the cricket team plays every 320 days and the basketball team plays every 400 days, so for finding the next time when both teams will play again we need to find the LCM of 320 and 400.
So, LCM of 320 and 400 is 1600.

Sammy's company prints 320 textbooks at a time. Daniel's company prints textbooks in sets of 400 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 320 and 400.
So, LCM of 320 and 400 is 1600.

Ariel exercises every 320 days and Rubel every 400 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 320 and 400 is 1600.

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

Greatest common factors or gcf of 320 and 400 is GCF(320, 400) * LCM(320, 400) = (320 x 400) / GCF(320, 400) = 1600.

Find the least number which is exactly divisible by 320 and 400.

Least number which is exactly divisible by 320 and 400 is 1600.

What is LCM of 320 and 400?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 320 and 400 by Listing Method

Example: Find lcm of 320 and 400 by Listing Method

Steps to find LCM of 320 and 400 by Common Division Method

Example: Find lcm of 320 and 400 by Common Division Method

Steps to find lcm of 320 and 400 by Formula

Example: Find lcm of 320 and 400 by Formula

Examples

What is LCM of 320 and 400?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 320 and 400 by Listing Method

Example: Find lcm of 320 and 400 by Listing Method

Steps to find LCM of 320 and 400 by Common Division Method

Example: Find lcm of 320 and 400 by Common Division Method

Steps to find lcm of 320 and 400 by Formula

Example: Find lcm of 320 and 400 by Formula

Examples

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