LCM of 8 and 64 is 64. LCM represents the smallest common multiple of two or more numbers. The article LCM of Two Numbers has been crafted by experts in a very simple and precise format describing the LCM concept quite effectively. Following this article while solving the problems is one of the best ways to strengthen and retain the concepts. Let us grasp the method of finding the least common multiple of 8 and 64 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 8 and 64?
The Least Common Multiple of 8 and 64 is 64.
How to Find LCM of 8 and 64?
LCM of 8 and 64 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 8 and 64 Using Prime Factorisation Method
In this method, the given natural numbers are written as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 8 and 64 can be represented as;
8 = 2 × 2 × 2
64 = 2 × 2 × 2 × 2 × 2 × 2
LCM (8, 64) = 2 × 2 × 2 × 2 × 2 × 2 = 64
LCM of 8 and 64 Using Division Method
In the division method, to determine the least common multiple of 8 and 64, we divide the numbers 8 and 64 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 8 and 64.
| 2 | 8 | 64 |
| 2 | 4 | 32 |
| 2 | 2 | 16 |
| 2 | 1 | 8 |
| 2 | 1 | 4 |
| 2 | 1 | 2 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (8, 64) = 2 × 2 × 2 × 2 × 2 × 2 = 64
LCM of 8 and 64 Using Listing the Multiples
Here, we list down the multiples of given numbers to determine the lowest common multiple among them. Check the multiples of 8 and 64 from the table mentioned below.
| Multiples of 8 | Multiples of 64 |
| 8 | 64 |
| 16 | 128 |
| 24 | 192 |
| 32 | 256 |
| 40 | 320 |
| 48 | 384 |
| 56 | 448 |
| 64 | 512 |
| 72 | 576 |
| 80 | 640 |
LCM (8, 64) = 64
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 8 and 64?
Solution: 64 is the smallest number that is divisible by both 8 and 64.
2. The GCD and LCM of the two numbers are 8 and 64. If one number is 8, calculate the other number.
Solution: Let the other number be z
We know that,
GCD × LCM = 8 × z
z = (GCD × LCM) / 8
z = (8 × 64) / 8
z = 64
Hence the other number is 64
Frequently Asked Questions on LCM of 8 and 64
What is the LCM of 8 and 64?
Write the difference between the LCM of 8 and 64 and the HCF of 8 and 64.
4 is the greatest common factor of 8 and 64. True or False.
What are the methods used to find the LCM of 8 and 64?
The methods used to find the LCM of 8 and 64 are
Prime Factorisation
Division Method
Listing the Multiples
If the LCM of 8 and 64 is 64. What is their GCF?
GCF × LCM = 8 × 64
Given
LCM = 64
GCF × 64 = 8 × 64
GCF = 8
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