LCM of 21 and 33 is 231. LCM denotes the least common factor or multiple of any two or more given numbers. Subject experts explained the LCM concept in simple language by keeping in mind the intelligence quotient of students. Using the article Lowest Common Multiple (LCM) on a regular basis help students to solve even the toughest problems in a shorter duration. In this article, let us learn how to represent the least common multiple of 21 and 33 with a complete explanation.
What is LCM of 21 and 33?
The Least Common Multiple of 21 and 33 is 231.
How to Find LCM of 21 and 33?
LCM of 21 and 33 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 21 and 33 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 21 and 33 are expressed as;
21 = 3 × 7
33 = 3 × 11
LCM (21, 33) = 3 × 7 × 11 = 231
LCM of 21 and 33 Using Division Method
In the division method, to find the least common multiple of 21 and 33, we divide the numbers 21 and 33 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 21 and 33.
| 3 | 21 | 33 |
| 7 | 7 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (21, 33) = 3 × 7 × 11 = 231
LCM of 21 and 33 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 21 and 33 are as follows:
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, ……………
Multiples of 33: 33, 66, 99, 132, 165, 198, 231, ……….
LCM (21, 33) = 231
Related Articles
Prime Factorisation 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 33?
Solution: 231 is the smallest number that is divisible by both 21 and 33.
2. The GCD and LCM of the two numbers are 3 and 231. If one number is 21, what is the other number?
Solution: Let the other number be k.
We know that
GCD × LCM = 21 × k
k = (GCD × LCM) / 21
k = (3 × 231) / 21
k = 33
Therefore, the other number is 33.
Frequently Asked Questions on LCM of 21 and 33
What is the LCM of 21 and 33?
Is the LCM of 21 and 33 the same as the HCF of 21 and 33?
Name the methods used to find the LCM of 21 and 33.
The methods used to find the LCM of 21 and 33 are as follows:
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 21 and 33 is 231?
GCF × LCM = 21 × 33
Given
LCM = 231
GCF × 231 = 21 × 33
GCF = 3
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