LCM of 42 and 66 is 462. LCM is termed as the least common multiple of any two or more given natural numbers. Students who find obstacles in determining the least common multiple of given numbers are recommended to follow the article LCM with Examples designed by experts. This article provides a detailed explanation of the LCM concept in simple language to make learning and understanding the concept an easy task. Let us learn how to verify the least common multiple of 42 and 66 using a simple technique in this article.
What is LCM of 42 and 66?
The answer to this question is 462.
How to Find LCM of 42 and 66?
LCM of 42 and 66 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 42 and 66 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 42 and 66 can be expressed as;
42 = 2 × 3 × 7
66 = 2 × 3 × 11
LCM (42, 66) = 2 × 3 × 7 × 11 = 462
LCM of 42 and 66 Using Division Method
In this method, we divide the numbers 42 and 66 by a common prime number until the remainder is a prime number or one. The product of these divisors represents the least common multiple of 42 and 66.
| 2 | 42 | 66 |
| 3 | 21 | 33 |
| 7 | 7 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (42, 66) = 2 × 3 × 7 × 11 = 462
LCM of 42 and 66 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 42 and 66.
| Multiples of 42 | Multiples of 66 |
| 42 | 66 |
| 84 | 132 |
| 126 | 198 |
| 168 | 264 |
| 210 | 330 |
| 252 | 396 |
| 294 | 462 |
| 336 | 528 |
| 378 | 594 |
| 420 | 660 |
| 462 | 726 |
LCM (42, 66) = 462
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 both 42 and 66?
Solution: The smallest number that is divisible by both 42 and 66 is their LCM. The LCM of 42 and 66 is 462. Hence, the smallest number that is divisible by both 42 and 66 is 462.
Frequently Asked Questions on LCM of 42 and 66
What is the LCM of 42 and 66?
Is the LCM of 42 and 66 and the HCF of 42 and 66 are same?
How do you find the LCM of 42 and 66 by the prime factorisation method?
In this method, the given natural numbers are expressed as the product of prime factors.
42 = 2 × 3 × 7
66 = 2 × 3 × 11
LCM (42, 66) = 2 × 3 × 7 × 11 = 462
What is the GCF if the LCM of 42 and 66 is 462?
GCF × LCM = 42 × 66
Given
GCF × 462 = 42 × 66
GCF = 6
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