LCM of 21 and 35 is 105. The value of LCM is the number evenly divisible by the given two numbers. Least common multiple of 21 and 35 is the number which is the smallest obtained from the common multiples. (21, 42, 63, 84, 105, 126, ….) and (35, 70, 105, 140, 175,….) are the multiples of 21 and 35. The LCM can be easily determined using methods such as prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 21 and 35?
The answer to this question is 105. The LCM of 21 and 35 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 21 and 35, is the smallest positive integer 105 which is divisible by both 21 and 35 with no remainder.
How to Find LCM of 21 and 35?
LCM of 21 and 35 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 35 Using Prime Factorisation Method
The prime factorisation of 21 and 35, respectively, is given by:
21 = 3 x 7 = 3¹ x 7¹
35 = 5 x 7 = 5¹ x 7¹
LCM (21, 35) = 105
LCM of 21 and 35 Using Division Method
We’ll divide the numbers (21, 35) by their prime factors to get the LCM of 21 and 35 using the division method (preferably common). The LCM of 21 and 35 is calculated by multiplying these divisors.
| 5 | 21 | 35 |
| 3 | 21 | 7 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (21, 35) = 105
LCM of 21 and 35 Using Listing the Multiples
To calculate the LCM of 21 and 35 by listing out the common multiples, list the multiples as shown below.
| Multiples of 21 | Multiples of 35 |
| 21 | 35 |
| 42 | 70 |
| 63 | 105 |
| 84 | 140 |
| 105 | 175 |
The smallest common multiple of 21 and 35 is 105.
Therefore LCM (21, 35) = 105
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Video Lesson on Applications of LCM
LCM of 21 and 35 Solved Example
What is the LCM if the GCD is 7 and the product of two numbers is 735?
Solution:
It is given that
Product of two numbers = 735
GCD = 7
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 735/7
LCM = 105
Hence, the LCM is 105.
Frequently Asked Questions on LCM of 21 and 35
What is the LCM of 21 and 35?
What are the methods used to calculate the LCM of 21 and 35?
Calculate the GCF if the LCM of 21 and 35 is 105.
LCM x GCF = 21 x 35
Given
LCM of 21 and 35 = 105
105 x GCF = 735
GCF = 735/105 = 7
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