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.
2 |
35 |
42 |
3 |
35 |
21 |
5 |
35 |
7 |
7 |
7 |
7 |
x |
1 |
1 |
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
![](https://cdn1.byjus.com/wp-content/uploads/2022/04/Application-of-LCM.jpg)
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.
Frequently Asked Questions on LCM of 35 and 42
Find the LCM of 35 and 42 using the prime factorization method.
To find the LCM using the prime factorization, we first have to determine the prime factors.
35 = 5 x 7
42 = 2 x 3 x 7
LCM of 35 and 42 is the product of prime factors raised to the highest exponent among the numbers 35 and 42
LCM of 35 and 42 = 210
If the LCM of 35 and 42 is 210, what is the GCF?
LCM x GCF = 35 x 42
Given
LCM of 35 and 42 = 210
210 x GCF = 1470
GCF = 1470/210 = 7
What is the relation between GCF and LCM of 35 and 42?
The relation between GCF and LCM of 35 and 42 is
LCM x GCF = 35 x 42
LCM x GCF = 1470
The LCM and GCD of two numbers are 210 and 7 respectively. If 42 is one number, determine the other.
Consider m as the other number.
LCM x GCD = 42 x m
m = (LCM x GCD)/42
m = (7 x 210)/ 42
m = 35
Hence, the other number is 35.
If the product of two numbers is 1470 and GCD is 7 calculate the LCM.
Given
Product = 1470
GCD = 7
LCM x GCD = product of two numbers
LCM = Product/GCD = 1470/7
LCM = 210
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