# What is LCM of 54 and 72?

LCM of 54 and 72 is 216

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 54 and 72 By Listing Method 3.   Steps to find LCM of 54 and 72 By Common Division Method 4.   Steps to find LCM of 54 and 72 By Formula 5.   Examples

#### What is LCM?

In mathematics, least common multiple, which is ordinarily reffered to as LCM is characterized as the smallest non-zero number which is divisible by both given numbers 54 and 72.

#### Properties of LCM

• LCM follows associative property, that means LCM(54, 72) = LCM(72, 54).
• 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 54 and 72 is 216, where 54 and 72 are less than 216.
• The LCM of two or more prime numbers is their product.

### Example: Find lcm of 54 and 72 by Listing Method

• Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540, 594, 648, 702, 756, 810, 864, 918, 972, 1026, 1080, 1134, 1188, 1242, 1296, 1350, 1404, 1458, 1512, 1566, 1620, 1674, 1728, 1782, 1836, 1890, 1944, 1998, 2052, 2106, 2160, 2214, 2268, 2322, 2376, 2430, 2484, 2538, 2592, 2646, 2700, 2754, 2808, 2862, 2916, 2970, 3024, 3078, 3132, 3186, 3240, 3294, 3348, 3402, 3456, 3510, 3564, 3618, 3672, 3726, 3780, 3834, 3888
• 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

Hence, LCM of 54 and 72 is 216.

### Example: Find lcm of 54 and 72 by Common Division Method

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

Hence, LCM of 54 and 72 is 2 x 2 x 2 x 3 x 3 x 3 = 216.

### Example: Find lcm of 54 and 72 by Formula

• GCF of 54 and 72 = 18
• LCM of 54 and 72 = (54 x 72) / 18
• => 3888 / 18

Hence, LCM of 54 and 72 is 216.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 54 and 72 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 54 and 72 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 54 and 72.
So, LCM of 54 and 72 is 216.

A shopkeeper sells candies in packet of 54 and chocolates in packet of 72. 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 54 and 72.
So, LCM of 54 and 72 is 216.

Both the cricket team and the rugby team had games, today. The cricket team plays every 54 days and the basketball team plays every 72 days. When will both teams have games on the same day again?

Given that the cricket team plays every 54 days and the basketball team plays every 72 days, so for finding the next time when both teams will play again we need to find the LCM of 54 and 72.
So, LCM of 54 and 72 is 216.

Freddy saves 54 dollars every day while Nikki saves 72 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 54 and 72.
So, LCM of 54 and 72 is 216.

Boxes that are 54 inches tall are being pilled next to boxes that are 72 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 54 and 72.
So, LCM of 54 and 72 is 216.

Sammy's company prints 54 textbooks at a time. Daniel's company prints textbooks in sets of 72 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 54 and 72.
So, LCM of 54 and 72 is 216.

Ariel exercises every 54 days and Rubel every 72 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 54 and 72 is 216.