Solved Example on LCM of 8 and 12

Some examples on LCM of 8 and 12

Example 1: Find the LCM if the product of two numbers is 96 and the GCD is 4.

Solution:

Given,

• Product of Two Numbers = 96
• GCD = 4

We know, LCM × GCD = Product of Two Numbers

LCM = Product/GCD

LCM = 96/4

LCM = 24

Example 2: Verify the relationship between GCF and LCM of 8 and 12.

Solution:

LCM(8, 12) × GCF(8, 12) = Product of 8, 12

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3

LCM (8, 12) = 2³ × 3= 24

HCF (8, 12) = 2² = 4

LCM (8, 12) × HCF (8, 12) = 24 × 4= 96

Product of 8, 12= 8 × 12= 96

Example 3: GCD and LCM of two numbers are 4 and 24 respectively. If one number is 8, find the other number.

Solution:

Let other number be x

GCD × LCM = 8 × x

x = (GCD × LCM)/8

x = (4 × 24)/8

x = 12

Therefore, the other number is 12.

Example 4: How to Find the LCM of 8 and 12 by Prime Factorization?

Solution:

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3

LCM (8, 12) = 24

LCM of 8 and 12 is 24. LCM is called Lest Common Multiple. The LCM of two non-zero integers, 8 and 12, is the smallest positive integer 24 which is divisible by both 8 and 12 with no remainder.

In this article, we will learn about what is the LCM of 8 and 12, What is LCM, and How to Find LCM of 8 and 12 using various methods like Prime factorization, Listing Multiples, and By Long Division Method.