LCM of 21 and 49 is 147. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. The article LCM of Two Numbers is an outstanding study resource for the students who aspire to clear their doubts based on the LCM instantly. Referring to this article while solving the problems helps students to understand the concept in a better way and lays a great foundation for their future studies. Here, we will learn how to verify the least common multiple of 21 and 49 in detail.
What is LCM of 21 and 49?
The Least Common Multiple of 21 and 49 is 147.
How to Find LCM of 21 and 49?
The LCM of 21 and 49 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 21 and 49 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 21 and 49 can be represented as;
21 = 3 × 7
49 = 7 × 7
LCM (21, 49) = 3 × 7 × 7 = 147
LCM of 21 and 49 Using Division Method
In the division method, we divide the numbers 21 and 49 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 21 and 49.
| 3 | 21 | 49 |
| 7 | 7 | 49 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (21, 49) = 3 × 7 × 7 = 147
LCM of 21 and 49 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 21 and 49.
| Multiples of 21 | Multiples of 49 |
| 21 | 49 |
| 42 | 98 |
| 63 | 147 |
| 84 | 196 |
| 105 | 245 |
| 126 | 294 |
| 147 | 343 |
| 168 | 392 |
LCM (21, 49) = 147
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 21 and 49?
Solution: 147 is the smallest number that is divisible by both 21 and 49.
2. What is the LCM if the product of two numbers is 1029 and their GCD is 7?
Solution: Given
GCD = 7
Product of numbers = 1029
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 1029 / 7
LCM = 147
Therefore the LCM is 147.
Frequently Asked Questions on LCM of 21 and 49
What is the LCM of 21 and 49?
What are the methods to find the LCM of 21 and 49?
The following methods are used to find the LCM of 21 and 49:
Prime Factorisation
Division Method
Listing the Multiples
7 is the HCF of 21 and 49. True or False.
Find the LCM of 21 and 49 using prime factorisation.
In prime factorisation, to find the LCM, we write the numbers as the product of prime factors
21 = 3 × 7
49 = 7 × 7
LCM (21, 49) = 3 × 7 × 7 = 147
Calculate the GCF if the LCM of 21 and 49 is 147.
GCF × LCM = 21 × 49
Given
LCM = 147
GCF × 147 = 21 × 49
GCF = 7
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