LCM of 56 and 84 is 168. LCM denotes the smallest positive number that is a multiple of two or more numbers. The Least Common Multiple (LCM) article is prepared by faculty to provide students with top-quality materials for reference. Students are recommended to use this article to master the LCM concept. Here, we will explain how to find the least common multiple of 56 and 84 with solved examples and FAQs.
What is LCM of 56 and 84?
The Least Common Multiple of 56 and 84 is 168.
How to Find LCM of 56 and 84?
LCM of 56 and 84 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 56 and 84 Using Prime Factorisation Method
In the prime factorisation method, LCM of 56 and 84 can be obtained by multiplying prime factors raised to their respective highest power.
56 = 2 × 2 × 2 × 7
84 = 2 × 2 × 3 × 7
LCM (56, 84) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 56 and 84 Using Division Method
In the division method, to find the LCM, we divide the numbers 56 and 84 by their prime factors until we get the result as one in the complete row. The product of these divisors indicates the least common multiple of 56 and 84.
| 2 | 56 | 84 |
| 2 | 28 | 42 |
| 2 | 14 | 21 |
| 3 | 7 | 21 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (56, 84) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 56 and 84 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the least common multiple among them. The below table shows the multiples of 56 and 84.
| Multiples of 56 | Multiples of 84 |
| 56 | 84 |
| 112 | 168 |
| 168 | 252 |
| 224 | 336 |
| 280 | 420 |
LCM (56, 84) = 168
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 56 and 84?
Solution: 168 is the smallest number that is divisible by both 56 and 84.
2. The GCD and LCM of the two numbers are 28 and 168. If one number is 84, what is the other number?
Solution: Let the other number be p
We know that,
GCD × LCM = 84 × p
p = (GCD × LCM) / 84
p = (28 × 168) / 84
p = 56
Thus the other number is 56.
Frequently Asked Questions on LCM of 56 and 84
What is the LCM of 56 and 84?
Mention the LCM of 56 and 84 and the HCF of 56 and 84.
Name the methods used to find the least common multiple of 56 and 84.
The following methods are used to find the least common multiple of 56 and 84:
Prime Factorisation
Division method
Listing the Multiples
What are the common factors of 56 and 84?
What is the GCF if the LCM of 56 and 84 is 168?
GCF × LCM = 56 × 84
Given
LCM = 168
GCF × 168 = 56 × 84
GCF = 28
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