LCM of 30 and 54

LCM of 30 and 54 is 270. The terms Least Common Divisor, Least Common multiple or Lowest common multiple simply known as LCD/ LCM is the smallest number that is a common to the multiples of both numbers. In the given set of numbers 30 and 54, 270 is the first (least or smallest) number that is common in the set of multiples of 30 and 54. You can use the HCF and LCM link to understand the difference between HCF and LCM. 

What is LCM of 30 and 54

The Least Common Multiple or Lowest Common Multiple of 30 and 54 is 270.

How to Find LCM of 30 and 54?

LCM of 30 and 54 can be determined using three methods:

• Prime Factorisation
• Division method
• Listing the multiples

LCM of 30 and 54 Using Prime Factorisation Method

In the Prime Factorisation method, 

1. Express the numbers as a product of prime factors
2. Common prime factors and their product forms the LCM

Here, 30 and 54 can be expressed as;

30 = 2 × 3 × 5

54 = 2 × 3 × 3 × 3

LCM (30, 54) = 2 × 3 × 3 × 3 × 5 = 270

LCM of 30 and 54 Using Division Method

In the Division Method, 

1. Divide the numbers starting with the smallest prime factor, say 2.
2. Continue division until the remainders is 1, by increasing the prime factors in the division. 
3. Product of prime factors = LCM.

Division method shown below;

LCM (30, 54) = 2 × 3 × 3 × 3 × 5 = 270

LCM of 30 and 54 Using Listing the Multiples

By listing all the multiples, we get the smallest common multiple from the list that forms the LCM. 

Below is the list of multiples for 30 and 54

LCM (30, 54) = 2 × 3 × 3 × 3 × 5 = 270

Related Articles

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

Video Lesson on Applications of LCM

Solved Examples 

What is the smallest number that is divisible by both 30 and 54?

Answer: 270 is the smallest number that is divisible by both 30 and 54. 

What is the LCM for 3, 10, 30 and 54? 

Answer: LCM for 3, 10, 30 and 54 is 270 as 3 and 10 are the factors of 30 and 3 is a factor of 54.