LCM of 30 and 42

LCM of 30 and 42 is 210. Students can memorize the steps used in determining the least common multiple of 30 and 42 by considering the common multiples. (30, 60, 90, 120, 150, 180, ….) and (42, 84, 126, 168, 210, 252,….) are the multiples of 30 and 42. The LCM of two numbers using methods such as prime factorisation, by listing the multiples and division are given here in a systematic manner.

Also read: Least common multiple

What is LCM of 30 and 42?

The answer to this question is 210. The LCM of 30 and 42 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 30 and 42, is the smallest positive integer 210 which is divisible by both 30 and 42 with no remainder.

How to Find LCM of 30 and 42?

LCM of 30 and 42 can be found using three methods:

• Prime Factorisation
• Division method
• Listing the multiples

LCM of 30 and 42 Using Prime Factorisation Method

The prime factorisation of 30 and 42, respectively, is given by:

30 = 2¹ x 3¹ x 5¹ 

42 = 2¹ x 3¹ x 7¹

LCM (30, 42) = 210

LCM of 30 and 42 Using Division Method

We’ll divide the numbers (30, 42) by their prime factors to get the LCM of 30 and 42 using the division method (preferably common). The LCM of 30 and 42 is calculated by multiplying these divisors.

No further division can be done. 

Hence, LCM (30, 42) = 210

LCM of 30 and 42 Using Listing the Multiples

To calculate the LCM of 30 and 42 by listing out the common multiples, list the multiples as shown below.

LCM (30, 42) = 210

Related Articles

• Prime Factorization and Division Method for LCM and HCF
• Prime Factors
• Properties of HCF and LCM
• LCM Formula

Video Lesson on Applications of LCM

LCM of 30 and 42 Solved Examples 

Question: If the GCD is 6 and the product of two numbers is 1260, find the LCM.

Solution:

It is given that,

GCD = 6

Product of two numbers = 1260

We know that;

LCM x GCD = product of two numbers

LCM = product of two numbers/ GCD

LCM = 1260/6

LCM = 210

Hence, the LCM is 210.