LCM of 48 and 72

LCM of 48 and 72 is 144. The Least Common Divisor (LCD) also known as Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 48 and 72, 144 is the first(least or smallest) number that is common in the set of multiples of 48 and 72. You can refer to Multiples.

What is LCM of 48 and 72

The Least Common Multiple or Lowest Common Multiple of 48 and 72 is 144.

How to Find LCM of 48 and 72?

LCM of 48 and 72 can be determined using three methods:

• Prime Factorisation
• Division method
• Listing the multiples

LCM of 48 and 72 Using Prime Factorisation Method

In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 48 and 72 can be expressed as;

48 = 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3 

LCM (48, 72) = 2 x 2 x 2 x 2 x 3 x 3 = 144

LCM of 48 and 72 Using Division Method

In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left. 

LCM (48, 72) = 2 x 2 x 2 x 2 x 3 x 3 = 144

LCM of 48 and 72 Using Listing the Multiples

By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 48 and 72

LCM (48, 72) = 144

Related Articles

• LCM
• LCM Calculator
• LCM Formula
• LCM with Examples
• HCF and LCM
• Prime Factorization and Division method

Video Lesson on Applications of LCM

Solved Examples 

What is the smallest number that is divisible by both 48 and 72?

Answer: 144 is the smallest number that is divisible by both 48 and 72. 

What is the LCM for 2, 48 and 72? 

Answer: LCM for 2, 48 and 72 is 144.