# What is LCM of 72 and 108?

LCM of 72 and 108 is 216

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 72 and 108 By Listing Method 3.   Steps to find LCM of 72 and 108 By Common Division Method 4.   Steps to find LCM of 72 and 108 By Formula 5.   Examples

#### 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 72 and 108

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 72 and 108 is 216, where 72 and 108 are less than 216.
• LCM is associative which means LCM(72, 108) = LCM(108, 72).
• 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.

### Example: Find lcm of 72 and 108 by Listing Method

• Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008, 1080, 1152, 1224, 1296, 1368, 1440, 1512, 1584, 1656, 1728, 1800, 1872, 1944, 2016, 2088, 2160, 2232, 2304, 2376, 2448, 2520, 2592, 2664, 2736, 2808, 2880, 2952, 3024, 3096, 3168, 3240, 3312, 3384, 3456, 3528, 3600, 3672, 3744, 3816, 3888, 3960, 4032, 4104, 4176, 4248, 4320, 4392, 4464, 4536, 4608, 4680, 4752, 4824, 4896, 4968, 5040, 5112, 5184, 5256, 5328, 5400, 5472, 5544, 5616, 5688, 5760, 5832, 5904, 5976, 6048, 6120, 6192, 6264, 6336, 6408, 6480, 6552, 6624, 6696, 6768, 6840, 6912, 6984, 7056, 7128, 7200, 7272, 7344, 7416, 7488, 7560, 7632, 7704, 7776
• Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776

Hence, LCM of 72 and 108 is 216.

### Example: Find lcm of 72 and 108 by Common Division Method

 2 72 108 2 36 54 2 18 27 3 9 27 3 3 9 3 1 3 1 1

Hence, LCM of 72 and 108 is 2 x 2 x 2 x 3 x 3 x 3 = 216.

### Example: Find lcm of 72 and 108 by Formula

• GCF of 72 and 108 = 36
• LCM of 72 and 108 = (72 x 108) / 36
• => 7776 / 36

Hence, LCM of 72 and 108 is 216.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 72 and 108 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 72 and 108 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 72 and 108.
So, LCM of 72 and 108 is 216.

A shopkeeper sells candies in packet of 72 and chocolates in packet of 108. 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 72 and 108.
So, LCM of 72 and 108 is 216.

Both the cricket team and the rugby team had games, today. The cricket team plays every 72 days and the basketball team plays every 108 days. When will both teams have games on the same day again?

Given that the cricket team plays every 72 days and the basketball team plays every 108 days, so for finding the next time when both teams will play again we need to find the LCM of 72 and 108.
So, LCM of 72 and 108 is 216.

Sammy's company prints 72 textbooks at a time. Daniel's company prints textbooks in sets of 108 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 72 and 108.
So, LCM of 72 and 108 is 216.

Ariel exercises every 72 days and Rubel every 108 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 72 and 108 is 216.

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

Greatest common factors or gcf of 72 and 108 is GCF(72, 108) * LCM(72, 108) = (72 x 108) / GCF(72, 108) = 216.

Find the least number which is exactly divisible by 72 and 108.

Least number which is exactly divisible by 72 and 108 is 216.