LCM of 42 and 56 is 168. LCM can be defined as the smallest common multiple of two or more numbers. The article LCM of Two Numbers, formulated by experts, helps students to understand the LCM concept thoroughly, irrespective of their intelligence quotient. Referring to this article while solving problems enables students to improve skills vital from an exam point of view. In this article, let us learn how to verify the least common multiple of 42 and 56 in a comprehensive manner.
What is LCM of 42 and 56?
The Least Common Multiple of 42 and 56 is 168.
How to Find LCM of 42 and 56?
The following methods can be used to find the LCM of 42 and 56:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 42 and 56 Using Prime Factorisation Method
Using the prime factorisation method, the LCM of 42 and 56 can be obtained by multiplying prime factors raised to their respective highest power.
42 = 2 × 3 × 7
56 = 2 × 2 × 2 × 7
LCM (42, 56) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 42 and 56 Using Division Method
In this method, we divide the numbers 42 and 56 by their prime factors until we get the result as one in the complete row to verify the least common multiple of 42 and 56. The product of these divisors represents the least common multiple of 42 and 56.
| 2 | 42 | 56 |
| 2 | 21 | 28 |
| 2 | 21 | 14 |
| 3 | 21 | 7 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (42, 56) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 42 and 56 Using Listing the Multiples
Here, we list the multiples of 42 and 56 to calculate the LCM of 42 and 56. Let us have a look at the multiples of 42 and 56 from the table given below.
| Multiples of 42 | Multiples of 56 |
| 42 | 56 |
| 84 | 112 |
| 126 | 168 |
| 168 | 224 |
| 210 | 280 |
| 252 | 336 |
LCM (42, 56) = 168
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q 1: Find the smallest number that is divisible by both 42 and 56.
Solution: The smallest number that is divisible by both 42 and 56 is 168.
Q 2: The product of the two numbers is 2352. If their GCD is 14, calculate their LCM.
Solution: Given
GCD = 14
Product of two numbers = 2352
We know that,
LCM × GCD = product of two numbers
LCM = Product of two numbers / GCD
LCM = 2352 / 14
LCM = 168
Therefore the least common multiple is 168.
Frequently Asked Questions on LCM of 42 and 56
What is the LCM of 42 and 56?
Name the methods used to find the LCM of 42 and 56.
The methods used to find the LCM of 42 and 56 are:
Prime Factorisation
Division Method
Listing the Multiples
Calculate the LCM of 42 and 56 using prime factorisation.
42 = 2 × 3 × 7
56 = 2 × 2 × 2 × 7
LCM (42, 56) = 2 × 2 × 2 × 3 × 7 = 168
Therefore the least common multiple of 42 and 56 by prime factorisation is 168
Calculate the GCF if the LCM of 42 and 56 is 168.
GCF × LCM = 42 × 56
Given
LCM = 168
GCF × 168 = 42 × 56
GCF = 14
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