# What is LCM of 36 and 54?

LCM of 36 and 54 is 108

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 36 and 54 By Listing Method 3.   Steps to find LCM of 36 and 54 By Common Division Method 4.   Steps to find LCM of 36 and 54 By Formula 5.   Examples

#### What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 36 and 54.

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 36 and 54 is 108, where 36 and 54 are less than 108.
• LCM is associative which means LCM(36, 54) = LCM(54, 36).
• 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 36 and 54 by Listing Method

• Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1008, 1044, 1080, 1116, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728, 1764, 1800, 1836, 1872, 1908, 1944
• 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

Hence, LCM of 36 and 54 is 108.

### Example: Find lcm of 36 and 54 by Common Division Method

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

Hence, LCM of 36 and 54 is 2 x 2 x 3 x 3 x 3 = 108.

### Example: Find lcm of 36 and 54 by Formula

• GCF of 36 and 54 = 18
• LCM of 36 and 54 = (36 x 54) / 18
• => 1944 / 18

Hence, LCM of 36 and 54 is 108.

#### Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 36 and 54 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 36 and 54 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 36 and 54.
So, LCM of 36 and 54 is 108.

A shopkeeper sells candies in packet of 36 and chocolates in packet of 54. 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 36 and 54.
So, LCM of 36 and 54 is 108.

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

Greatest common factors or gcf of 36 and 54 is GCF(36, 54) * LCM(36, 54) = (36 x 54) / GCF(36, 54) = 108.

Sammy's company prints 36 textbooks at a time. Daniel's company prints textbooks in sets of 54 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 36 and 54.
So, LCM of 36 and 54 is 108.

Mary exercises every 36 days and Nikki every 54 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 36 and 54 is 108.

Find the least common multiple of 36 and 54.

Least common multiple of 36 and 54 is 108.

Find the least number which is exactly divisible by 36 and 54.

Least number which is exactly divisible by 36 and 54 is 108.