LCM of 54 and 64 is 1728. LCM can be defined as the smallest common multiple of two or more numbers. Least Common Multiple (LCM) is a major reference guide in solving problems relying on the LCM more effectively. The main purpose of creating this article is to help students improve their problem-solving and logical thinking skills, which are essential from an exam point of view. Here, let us grasp the simple method of how to find the least common multiple of 54 and 64 using solved examples.
What is LCM of 54 and 64?
The Least Common Multiple of 54 and 64 is 1728.
How to Find LCM of 54 and 64?
LCM of 54 and 64 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 54 and 64 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree.
54 = 2 × 3 × 3 × 3
64 = 2 × 2 × 2 × 2 × 2 × 2
LCM (54, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 1728
LCM of 54 and 64 Using Division Method
In the division method, to determine the least common multiple of 54 and 64, we divide the numbers 54 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 54 and 64.
| 2 | 54 | 64 |
| 2 | 27 | 32 |
| 2 | 27 | 16 |
| 2 | 27 | 8 |
| 2 | 27 | 4 |
| 2 | 27 | 2 |
| 3 | 27 | 1 |
| 3 | 9 | 1 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (54, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 1728
LCM of 54 and 64 Using Listing the Multiples
In this method, we list the multiples of 54 and 64 to find the least common multiple among them. The multiples of 54 and 64 are as follows:
Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540, ………., 1620, 1674, 1728,…
Multiples of 64: 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, ….., 1600, 1664, 1728,….
LCM (54, 64) = 1728
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 54 and 64?
Solution: 1728 is the smallest number that is divisible by both 54 and 64.
2. The GCD and LCM of the two numbers are 2 and 1728. If one number is 54, what is the other number?
Solution: Let the other number be p
We know that,
GCD × LCM = 54 × p
p = (GCD × LCM) / 54
p = (2 × 1728) / 54
p = 64
Hence the other number is 64.
Frequently Asked Questions on LCM of 54 and 64
What is the LCM of 54 and 64?
Mention the LCM of 54 and 64 and the HCF of 54 and 64.
Name the methods used to find the least common multiple of 54 and 64.
The methods used to find the least common multiple of 54 and 64 are as follows:
Prime Factorisation
Division method
Listing the Multiples
Write the relation between GCF and LCM of 54 and 64.
The below equation can be used to denote the relation between GCF and LCM of 54 and 64
GCF × LCM = 54 × 64
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