What is the LCM of 240 and 285 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 240 and 285, is defined as the smallest positive integer that is divisible by both. It is written as LCM(240, 285).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 240 and 285 is 4560, where 240 and 285 are less than 4560.
LCM is associative which means LCM(240, 285) = LCM(285, 240).
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 240 and 285 by Listing Method

Find some first multiples of 240 and 285.
Find the least common multiple, and read off the answer!

Example: Find lcm of 240 and 285 by Listing Method

Multiples of 240: 240, 480, 720, 960, 1200, 1440, 1680, 1920, 2160, 2400, 2640, 2880, 3120, 3360, 3600, 3840, 4080, 4320, 4560, 4800, 5040, 5280, 5520, 5760, 6000, 6240, 6480, 6720, 6960, 7200, 7440, 7680, 7920, 8160, 8400, 8640, 8880, 9120, 9360, 9600, 9840, 10080, 10320, 10560, 10800, 11040, 11280, 11520, 11760, 12000, 12240, 12480, 12720, 12960, 13200, 13440, 13680, 13920, 14160, 14400, 14640, 14880, 15120, 15360, 15600, 15840, 16080, 16320, 16560, 16800, 17040, 17280, 17520, 17760, 18000, 18240, 18480, 18720, 18960, 19200, 19440, 19680, 19920, 20160, 20400, 20640, 20880, 21120, 21360, 21600, 21840, 22080, 22320, 22560, 22800, 23040, 23280, 23520, 23760, 24000, 24240, 24480, 24720, 24960, 25200, 25440, 25680, 25920, 26160, 26400, 26640, 26880, 27120, 27360, 27600, 27840, 28080, 28320, 28560, 28800, 29040, 29280, 29520, 29760, 30000, 30240, 30480, 30720, 30960, 31200, 31440, 31680, 31920, 32160, 32400, 32640, 32880, 33120, 33360, 33600, 33840, 34080, 34320, 34560, 34800, 35040, 35280, 35520, 35760, 36000, 36240, 36480, 36720, 36960, 37200, 37440, 37680, 37920, 38160, 38400, 38640, 38880, 39120, 39360, 39600, 39840, 40080, 40320, 40560, 40800, 41040, 41280, 41520, 41760, 42000, 42240, 42480, 42720, 42960, 43200, 43440, 43680, 43920, 44160, 44400, 44640, 44880, 45120, 45360, 45600, 45840, 46080, 46320, 46560, 46800, 47040, 47280, 47520, 47760, 48000, 48240, 48480, 48720, 48960, 49200, 49440, 49680, 49920, 50160, 50400, 50640, 50880, 51120, 51360, 51600, 51840, 52080, 52320, 52560, 52800, 53040, 53280, 53520, 53760, 54000, 54240, 54480, 54720, 54960, 55200, 55440, 55680, 55920, 56160, 56400, 56640, 56880, 57120, 57360, 57600, 57840, 58080, 58320, 58560, 58800, 59040, 59280, 59520, 59760, 60000, 60240, 60480, 60720, 60960, 61200, 61440, 61680, 61920, 62160, 62400, 62640, 62880, 63120, 63360, 63600, 63840, 64080, 64320, 64560, 64800, 65040, 65280, 65520, 65760, 66000, 66240, 66480, 66720, 66960, 67200, 67440, 67680, 67920, 68160, 68400
Multiples of 285: 285, 570, 855, 1140, 1425, 1710, 1995, 2280, 2565, 2850, 3135, 3420, 3705, 3990, 4275, 4560, 4845, 5130, 5415, 5700, 5985, 6270, 6555, 6840, 7125, 7410, 7695, 7980, 8265, 8550, 8835, 9120, 9405, 9690, 9975, 10260, 10545, 10830, 11115, 11400, 11685, 11970, 12255, 12540, 12825, 13110, 13395, 13680, 13965, 14250, 14535, 14820, 15105, 15390, 15675, 15960, 16245, 16530, 16815, 17100, 17385, 17670, 17955, 18240, 18525, 18810, 19095, 19380, 19665, 19950, 20235, 20520, 20805, 21090, 21375, 21660, 21945, 22230, 22515, 22800, 23085, 23370, 23655, 23940, 24225, 24510, 24795, 25080, 25365, 25650, 25935, 26220, 26505, 26790, 27075, 27360, 27645, 27930, 28215, 28500, 28785, 29070, 29355, 29640, 29925, 30210, 30495, 30780, 31065, 31350, 31635, 31920, 32205, 32490, 32775, 33060, 33345, 33630, 33915, 34200, 34485, 34770, 35055, 35340, 35625, 35910, 36195, 36480, 36765, 37050, 37335, 37620, 37905, 38190, 38475, 38760, 39045, 39330, 39615, 39900, 40185, 40470, 40755, 41040, 41325, 41610, 41895, 42180, 42465, 42750, 43035, 43320, 43605, 43890, 44175, 44460, 44745, 45030, 45315, 45600, 45885, 46170, 46455, 46740, 47025, 47310, 47595, 47880, 48165, 48450, 48735, 49020, 49305, 49590, 49875, 50160, 50445, 50730, 51015, 51300, 51585, 51870, 52155, 52440, 52725, 53010, 53295, 53580, 53865, 54150, 54435, 54720, 55005, 55290, 55575, 55860, 56145, 56430, 56715, 57000, 57285, 57570, 57855, 58140, 58425, 58710, 58995, 59280, 59565, 59850, 60135, 60420, 60705, 60990, 61275, 61560, 61845, 62130, 62415, 62700, 62985, 63270, 63555, 63840, 64125, 64410, 64695, 64980, 65265, 65550, 65835, 66120, 66405, 66690, 66975, 67260, 67545, 67830, 68115, 68400

Hence, LCM of 240 and 285 is 4560.

Steps to find LCM of 240 and 285 by Common Division Method

Find all the prime numbers that would divide 240 and 285 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 240 and 285 by Common Division Method

2	240 285
2	120 285
2	60 285
2	30 285
3	15 285
5	5 95
19	1 19
	1 1

Hence, LCM of 240 and 285 is 2 x 2 x 2 x 2 x 3 x 5 x 19 = 4560.

Steps to find lcm of 240 and 285 by Formula

The formula for LCM is LCM (240, 285) = (240 x 285) / GCF (240, 285)
Apply the formula, and read off the answer!

Example: Find lcm of 240 and 285 by Formula

GCF of 240 and 285 = 15
LCM of 240 and 285 = (240 x 285) / 15
=> 68400 / 15

Hence, LCM of 240 and 285 is 4560.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 240 and 285 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 240 and 285 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 240 and 285.
So, LCM of 240 and 285 is 4560.

A shopkeeper sells candies in packet of 240 and chocolates in packet of 285. 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 240 and 285.
So, LCM of 240 and 285 is 4560.

Both the cricket team and the rugby team had games, today. The cricket team plays every 240 days and the basketball team plays every 285 days. When will both teams have games on the same day again?

Given that the cricket team plays every 240 days and the basketball team plays every 285 days, so for finding the next time when both teams will play again we need to find the LCM of 240 and 285.
So, LCM of 240 and 285 is 4560.

Sammy's company prints 240 textbooks at a time. Daniel's company prints textbooks in sets of 285 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 240 and 285.
So, LCM of 240 and 285 is 4560.

Ariel exercises every 240 days and Rubel every 285 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 240 and 285 is 4560.

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

Greatest common factors or gcf of 240 and 285 is GCF(240, 285) * LCM(240, 285) = (240 x 285) / GCF(240, 285) = 4560.

Find the least number which is exactly divisible by 240 and 285.

Least number which is exactly divisible by 240 and 285 is 4560.

What is LCM of 240 and 285?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 240 and 285 by Listing Method

Example: Find lcm of 240 and 285 by Listing Method

Steps to find LCM of 240 and 285 by Common Division Method

Example: Find lcm of 240 and 285 by Common Division Method

Steps to find lcm of 240 and 285 by Formula

Example: Find lcm of 240 and 285 by Formula

Examples

What is LCM of 240 and 285?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 240 and 285 by Listing Method

Example: Find lcm of 240 and 285 by Listing Method

Steps to find LCM of 240 and 285 by Common Division Method

Example: Find lcm of 240 and 285 by Common Division Method

Steps to find lcm of 240 and 285 by Formula

Example: Find lcm of 240 and 285 by Formula

Examples

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