LCM of 24 and 64 is 192. The lowest common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. The article Least Common Multiple (LCM) explains the concept in an easy to understand format to help students fetch high marks in their final exams. Following this article on a daily basis, students can strengthen and retain their concepts more effectively. Learn the simple method to find the least common multiple of 24 and 64 with a complete explanation in this article.
What is LCM of 24 and 64?
The Least Common Multiple of 24 and 64 is 192.
How to Find LCM of 24 and 64?
The LCM of 24 and 64 can be determined by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 24 and 64 Using Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as product of prime numbers. Hence the numbers 24 and 64 can be expressed as;
24 = 2 × 2 × 2 × 3
64 = 2 × 2 × 2 × 2 × 2 × 2
LCM (24, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192
LCM of 24 and 64 Using Division Method
In the division method, to find the LCM, we divide the numbers 24 and 64 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 24 and 64.
| 2 | 24 | 64 |
| 2 | 12 | 32 |
| 2 | 6 | 16 |
| 2 | 3 | 8 |
| 2 | 3 | 4 |
| 2 | 3 | 2 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192
LCM of 24 and 64 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the least common multiple among them. The following table shows the multiples of 24 and 64.
| Mutliples of 24 | Multiples of 64 |
| 24 | 64 |
| 48 | 128 |
| 72 | 192 |
| 96 | 256 |
| 120 | 320 |
| 144 | 384 |
| 168 | 448 |
| 192 | 512 |
| 216 | 576 |
LCM (24, 64) = 192
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 24 and 64?
Solution: 192 is the smallest number that is divisible by both 24 and 64.
2. The GCD and LCM of the two numbers are 8 and 192. If one number is 24, what is the other number?
Solution: Let the other number be p
We know that,
GCD × LCM = 24 × p
p = (GCD × LCM) / 24
p = (8 × 192) / 24
p = 64
Hence, the other number is 64.
Frequently Asked Questions on LCM of 24 and 64
What is the LCM of 24 and 64?
Is the LCM of 24 and 64 the same as the HCF of 24 and 64?
What is the greatest common factor of 24 and 64?
Determine the GCF if the LCM of 24 and 64 is 192.
GCF × LCM = 24 × 64
Given
LCM = 192
GCF × 192 = 24 × 64
GCF = 8
What are the methods used to find the LCM of 24 and 64?
The following methods are used to find the LCM of 24 and 64
Prime Factorisation
Division Method
Listing the Multiples
Comments