Example on LCM of 24 and 36

Some examples on LCM of 24 and 36

Example 1. Find the LCM if the product of two numbers is 864 and the GCD is 12.

Solution:

Given,

• Product of Two Numbers = 864
• GCD = 12

We know, LCM × GCD = Product of Two Numbers

LCM = Product/GCD

LCM = 864/12

LCM = 72

Example 2. Verify the relationship between GCF and LCM of 24 and 36.

Solution:

LCM(24, 36) × GCF(24, 36) = Product of 24, 36

• 24 = 2 × 2 × 2 × 3 = 2³ × 3
• 36 = 2 × 2 × 3 × 3 = 2² × 3²

LCM(24, 36) = 72

GCF(24, 36) = 12

LCM(24, 36) × GCF(24, 36) = 72 × 12 = 864

Product of 24, 36 = 24 × 36 = 864

Example 3. GCD and LCM of two numbers are 12 and 72 respectively. If one number is 24, find the other number.

Solution:

Let other number be x

GCD × LCM = 24 × x

x = (GCD × LCM)/24

x = (12 × 72)/24

x = 36

Therefore, the other number is 36.

Example 4. How to Find the LCM of 24 and 36 by Prime Factorization?

Solution:

24 = 2 x 2 x 2 x 3 = 2³ x 3

36 = 2 x 2 x 3 x 3 = 2² x 3²

LCM (24, 36) = 72

LCM of 24 and 36 is 72. LCM of two non-zero integers, 24 and 36, is the smallest positive integer 72 which is divisible by both 24 and 36 with no remainder.

In this article, we will learn about what is the LCM of 24 and 36, What is LCM, and How to Find LCM of 24 and 36 using various methods like Prime factorization, Listing Multiples, and By Long Division Method.