# What is LCM of 24 and 36?

LCM of 24 and 36 is 72

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 24 and 36 By Listing Method 3.   Steps to find LCM of 24 and 36 By Common Division Method 4.   Steps to find LCM of 24 and 36 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 24 and 36.

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 24 and 36 is 72, where 24 and 36 are less than 72.
• LCM is associative which means LCM(24, 36) = LCM(36, 24).
• 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 24 and 36 by Listing Method

• Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720, 744, 768, 792, 816, 840, 864
• 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

Hence, LCM of 24 and 36 is 72.

### Example: Find lcm of 24 and 36 by Common Division Method

 2 24 36 2 12 18 2 6 9 3 3 9 3 1 3 1 1

Hence, LCM of 24 and 36 is 2 x 2 x 2 x 3 x 3 = 72.

### Example: Find lcm of 24 and 36 by Formula

• GCF of 24 and 36 = 12
• LCM of 24 and 36 = (24 x 36) / 12
• => 864 / 12

Hence, LCM of 24 and 36 is 72.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 24 and 36 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 24 and 36 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 24 and 36.
So, LCM of 24 and 36 is 72.

A shopkeeper sells candies in packet of 24 and chocolates in packet of 36. 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 24 and 36.
So, LCM of 24 and 36 is 72.

Both the cricket team and the rugby team had games, today. The cricket team plays every 24 days and the basketball team plays every 36 days. When will both teams have games on the same day again?

Given that the cricket team plays every 24 days and the basketball team plays every 36 days, so for finding the next time when both teams will play again we need to find the LCM of 24 and 36.
So, LCM of 24 and 36 is 72.

Sammy's company prints 24 textbooks at a time. Daniel's company prints textbooks in sets of 36 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 24 and 36.
So, LCM of 24 and 36 is 72.

Ariel exercises every 24 days and Rubel every 36 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 24 and 36 is 72.

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

Greatest common factors or gcf of 24 and 36 is GCF(24, 36) * LCM(24, 36) = (24 x 36) / GCF(24, 36) = 72.

Find the least number which is exactly divisible by 24 and 36.

Least number which is exactly divisible by 24 and 36 is 72.