LCM of 3, 9 and 21 is 63. LCM denotes the least common factor or multiple of any two or more given numbers. The article Lowest Common Multiple (LCM) is formulated by an expert teacher having vast knowledge of the LCM concept. Students aiming to obtain a thorough knowledge of the LCM concept can refer to this article which is the best guide any student can rely on. In this article, we will learn how to find the least common multiple of 3, 9 and 21 using solved examples and FAQs.
What is LCM of 3, 9 and 21?
The Least Common Multiple of 3, 9 and 21 is 63.
How to Find LCM of 3, 9 and 21?
LCM of 3, 9 and 21 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 3, 9 and 21 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 3, 9 and 21 are expressed as;
3 = 3
9 = 3 × 3
21 = 3 × 7
LCM (3, 9, 21) = 3 × 3 × 7 = 63
LCM of 3, 9 and 21 Using Division Method
In the division method, to find the least common multiple of 3, 9 and 21, we divide the numbers 3, 9 and 21 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 3, 9 and 21.
| 3 | 3 | 9 | 21 |
| 3 | 1 | 3 | 7 |
| 7 | 1 | 1 | 7 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (3, 9, 21) = 3 × 3 × 7 = 63
LCM of 3, 9 and 21 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. The multiples of 3, 9 and 21 are as follows:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ………., 57, 60, 63, ………
Multiples of 9: 9, 18, 27, 36, 45, 54, 63,…. …….
Multiples of 21: 21, 42, 63, ……………….
LCM (3, 9, 21) = 63
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 3, 9, 21 exactly?
Solution: The smallest number that is divisible by 3, 9, 21 exactly is their LCM. The LCM of 3, 9 and 21 is 63. Hence the smallest number that is divisible by 3, 9, 21 exactly is 63.
Frequently Asked Questions on LCM of 3, 9 and 21
What is the LCM of 3, 9 and 21?
Is the LCM of 3, 9 and 21 and the HCF of 3, 9 and 21 are same?
Name the methods used to find the LCM of 3, 9 and 21.
The methods used to find the LCM of 3, 9 and 21 are:
Prime Factorisation
Division method
Listing the Multiples
Using prime factorisation, determine the LCM of 3, 9 and 21.
In this method, we express the numbers as the product of prime factors to determine the LCM
3 = 3
9 = 3 × 3
21 = 3 × 7
LCM (3, 9, 21) = 3 × 3 × 7 = 63
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