A day full of math games & activities. Find one near you.

LCM of 54 and 64

LCM of 54 and 64 is the smallest number among all common multiples of 54 and 64. The first few multiples of 54 and 64 are (54, 108, 162, 216, 270, . . . ) and (64, 128, 192, 256, . . . ) respectively. There are 3 commonly used methods to find LCM of 54 and 64 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 54 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 54 and 64?

Answer: LCM of 54 and 64 is 1728.

Explanation:

The LCM of two non-zero integers, x(54) and y(64), is the smallest positive integer m(1728) that is divisible by both x(54) and y(64) without any remainder.

Methods to Find LCM of 54 and 64

The methods to find the LCM of 54 and 64 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 54 and 64 by Division Method

To calculate the LCM of 54 and 64 by the division method, we will divide the numbers(54, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 54 and 64.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 54 and 64. Write this prime number(2) on the left of the given numbers(54 and 64), separated as per the ladder arrangement.
Step 2: If any of the given numbers (54, 64) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 54 and 64 is the product of all prime numbers on the left, i.e. LCM(54, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 1728.

LCM of 54 and 64 by Prime Factorization

Prime factorization of 54 and 64 is (2 × 3 × 3 × 3) = 2¹ × 3³ and (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ respectively. LCM of 54 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ × 3³ = 1728.
Hence, the LCM of 54 and 64 by prime factorization is 1728.

LCM of 54 and 64 by Listing Multiples

To calculate the LCM of 54 and 64 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 54 (54, 108, 162, 216, 270, . . . ) and 64 (64, 128, 192, 256, . . . . )
Step 2: The common multiples from the multiples of 54 and 64 are 1728, 3456, . . .
Step 3: The smallest common multiple of 54 and 64 is 1728.

∴ The least common multiple of 54 and 64 = 1728.

☛ Also Check:

LCM of 54 and 64 Examples

Example 1: Find the smallest number that is divisible by 54 and 64 exactly.

Solution:

The value of LCM(54, 64) will be the smallest number that is exactly divisible by 54 and 64.
⇒ Multiples of 54 and 64:
- Multiples of 54 = 54, 108, 162, 216, 270, 324, 378, 432, 486, 540, . . . ., 1512, 1566, 1620, 1674, 1728, . . . .
- Multiples of 64 = 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, . . . ., 1472, 1536, 1600, 1664, 1728, . . . .
Therefore, the LCM of 54 and 64 is 1728.
Example 2: The GCD and LCM of two numbers are 2 and 1728 respectively. If one number is 54, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 54 × b
⇒ b = (GCD × LCM)/54
⇒ b = (2 × 1728)/54
⇒ b = 64
Therefore, the other number is 64.
Example 3: Verify the relationship between GCF and LCM of 54 and 64.

Solution:

The relation between GCF and LCM of 54 and 64 is given as,
LCM(54, 64) × GCF(54, 64) = Product of 54, 64
Prime factorization of 54 and 64 is given as, 54 = (2 × 3 × 3 × 3) = 2¹ × 3³ and 64 = (2 × 2 × 2 × 2 × 2 × 2) = 2⁶
LCM(54, 64) = 1728
GCF(54, 64) = 2
LHS = LCM(54, 64) × GCF(54, 64) = 1728 × 2 = 3456
RHS = Product of 54, 64 = 54 × 64 = 3456
⇒ LHS = RHS = 3456
Hence, verified.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on LCM of 54 and 64

What is the LCM of 54 and 64?

The LCM of 54 and 64 is 1728. To find the least common multiple of 54 and 64, we need to find the multiples of 54 and 64 (multiples of 54 = 54, 108, 162, 216 . . . . 1728; multiples of 64 = 64, 128, 192, 256 . . . . 1728) and choose the smallest multiple that is exactly divisible by 54 and 64, i.e., 1728.

How to Find the LCM of 54 and 64 by Prime Factorization?

To find the LCM of 54 and 64 using prime factorization, we will find the prime factors, (54 = 2 × 3 × 3 × 3) and (64 = 2 × 2 × 2 × 2 × 2 × 2). LCM of 54 and 64 is the product of prime factors raised to their respective highest exponent among the numbers 54 and 64.
⇒ LCM of 54, 64 = 2⁶ × 3³ = 1728.

What is the Relation Between GCF and LCM of 54, 64?

The following equation can be used to express the relation between GCF and LCM of 54 and 64, i.e. GCF × LCM = 54 × 64.

If the LCM of 64 and 54 is 1728, Find its GCF.

LCM(64, 54) × GCF(64, 54) = 64 × 54
Since the LCM of 64 and 54 = 1728
⇒ 1728 × GCF(64, 54) = 3456
Therefore, the greatest common factor (GCF) = 3456/1728 = 2.

Which of the following is the LCM of 54 and 64? 18, 24, 1728, 2

The value of LCM of 54, 64 is the smallest common multiple of 54 and 64. The number satisfying the given condition is 1728.

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum