LCM of 21 and 56 is 168. The smallest number among all frequent multiples of 21 and 56 is the LCM of 21 and 56. (21, 42, 63, 84, 105, etc.) and (56, 112, 168, 224, etc.) are the first few multiples of 21 and 56, respectively. To find the LCM of 21 and 56, there are three typical methods: listing multiples, prime factorization, and division technique. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 21 and 56?
The answer to this question is 168. The LCM of 21 and 56 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 21 and 56, is the smallest positive integer 168 which is divisible by both 21 and 56 with no remainder.
How to Find LCM of 21 and 56?
LCM of 21 and 56 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 56 Using Prime Factorisation Method
The prime factorisation of 21 and 56, respectively, is given by:
21 = (3 × 7) = 31 × 71 and
56 = (2 × 2 × 2 × 7) = 23 × 71
LCM (21, 56) = 168
LCM of 21 and 56 Using Division Method
We’ll divide the numbers (21, 56) by their prime factors to get the LCM of 21 and 56 using the division method (preferably common). The LCM of 21 and 56 is calculated by multiplying these divisors.
| 2 | 21 | 56 |
| 2 | 21 | 28 |
| 2 | 21 | 14 |
| 3 | 21 | 7 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (21, 56) = 168
LCM of 21 and 56 Using Listing the Multiples
To calculate the LCM of 21 and 56 by listing out the common multiples, list the multiples as shown below.
| Multiples of 21 | Multiples of 56 |
| 21 | 56 |
| 42 | 112 |
| 63 | 168 |
| ….. | 224 |
| 168 | 280 |
The smallest common multiple of 21 and 56 is 168.
Therefore LCM (21, 56) = 168
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LCM of 21 and 56 Solved Example
The product of two numbers is 1176. If their GCD is 7, what is their LCM?
Solution:
Given: GCD = 7
product of numbers = 1176
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1176/7
Therefore, the LCM is 168.
The probable combination for the given case is LCM(21, 56) = 168.
Frequently Asked Questions on LCM of 21 and 56
What is the LCM of 21 and 56?
List the methods used to find the LCM of 21 and 56.
Which of the following is the LCM of 21 and 56? 21, 12, 168, 36
LCM(56, 21) × GCF(56, 21) = 56 × 21
⇒ 168 × GCF(56, 21) = 1176
Therefore, the greatest common factor (GCF) = 1176/168 = 7.
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