LCM of 35 and 42

LCM of 35 and 42 is 210. The smallest number among the common multiples of 35 and 42 gives you the LCM value. Least common multiples of 35 and 42 are obtained using the common multiples. (35, 70, 105, 140, 175, ….) and (42, 84, 126, 168, 210, 252, 294,….) are the multiples of 35 and 42. The LCM of two numbers using prime factorization, division and by listing the multiples are explained here for a better knowledge among students. 

Also read: Least common multiple

What is LCM of 35 and 42?

The answer to this question is 210. The LCM of 35 and 42 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 35 and 42, is the smallest positive integer 210 which is divisible by both 35 and 42 with no remainder.

How to Find LCM of 35 and 42?

LCM of 35 and 42 can be found using three methods:

• Prime Factorisation
• Division method
• Listing the multiples

LCM of 35 and 42 Using Prime Factorisation Method

The prime factorisation of 35 and 42, respectively, is given by:

35 = 5 x 7 = 5¹ x 7¹

42 = 2 x 3 x 7 = 2¹ x 3¹ x 7¹

LCM (35, 42) = 210

LCM of 35 and 42 Using Division Method

We’ll divide the numbers (35, 42) by their prime factors to get the LCM of 35 and 42 using the division method (preferably common). The LCM of 35 and 42 is calculated by multiplying these divisors.

No further division can be done. 

Hence, LCM (35, 42) = 210

LCM of 35 and 42 Using Listing the Multiples

To calculate the LCM of 35 and 42 by listing out the common multiples, list the multiples as shown below:

Multiples of 35 = 35, 70, 105, 140, 175, 210, …..

Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, …..

LCM (35, 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 35 and 42 Solved Examples 

Question: Find the smallest number exactly divisible by 35 and 42.

Solution:

We know that;

The smallest number which is exactly divisible by 35 and 42 is the LCM.

(35, 70, 105, 140, 175, 210, …..) are the multiples of 35

(42, 84, 126, 168, 210, 252, 294, …..) are the multiples of 42

Hence, the LCM of 35 and 42 is 210.