LCM of 60 and 42 is 420. LCM denotes the smallest positive number which is a multiple of two or more numbers. Subject experts explain the LCM concept in simple language so that students can learn it irrespective of their intelligence capacity. From the article Least Common Multiple (LCM), students will be able to solve the problems based on the LCM confidently. Let us grasp the simple method of how to find the least common multiple of 60 and 42 with solved examples and FAQs in a detailed manner.
What is LCM of 60 and 42?
The answer to this question is 420.
How to Find LCM of 60 and 42?
LCM of 60 and 42 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 60 and 42 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 60 and 42 can be expressed as;
60 = 2 × 2 × 3 × 5
42 = 2 × 3 × 7
LCM (60, 42) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 60 and 42 Using Division Method
In this method, we divide the numbers 60 and 42 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 60 and 42.
| 2 | 60 | 42 |
| 2 | 30 | 21 |
| 3 | 15 | 21 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (60, 42) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 60 and 42 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 60 and 42.
| Multiples of 60 | Multiples of 42 |
| 60 | 42 |
| 120 | 84 |
| 180 | 126 |
| 240 | 168 |
| 300 | 210 |
| 360 | 252 |
| 420 | 294 |
| 480 | 336 |
| 540 | 378 |
| 600 | 420 |
LCM (60, 42) = 420
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 60 and 42?
Solution: 420 is the smallest number that is divisible by both 60 and 42.
2. The GCD and LCM of the two numbers are 6 and 420. If one number is 60, what is the other number?
Solution: Let the other number be k
We know that,
GCD × LCM = 60 × k
k = (GCD × LCM) / 60
k = ( 6 × 420) / 60
k = 42
Hence the other number is 42.
Frequently Asked Questions on LCM of 60 and 42
What is the LCM of 60 and 42?
Is the LCM of 60 and 42 the same as the HCF of 60 and 42?
How to find the LCM of 60 and 42 by prime factorisation?
In the prime factorisation method, the given numbers are expressed as the product of prime factors
60 = 2 × 2 × 3 × 5
42 = 2 × 3 × 7
LCM (60, 42) = 2 × 2 × 3 × 5 × 7 = 420
Hence, 420 is the LCM of 60 and 42 by prime factorisation
Find the GCF if the LCM of 60 and 42 is 420.
GCF × LCM = 60 × 42
Given
LCM = 420
GCF × 420 = 60 × 42
GCF = 6
What are the methods used to find the LCM of 60 and 42?
The methods used to find the LCM of 60 and 42 are
Prime Factorisation
Division Method
Listing the Multiples
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