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LCM of 16 and 64

LCM of 16 and 64 is the smallest number among all common multiples of 16 and 64. The first few multiples of 16 and 64 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (64, 128, 192, 256, 320, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 64 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 16 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 16 and 64?

Answer: LCM of 16 and 64 is 64.

Explanation:

The LCM of two non-zero integers, x(16) and y(64), is the smallest positive integer m(64) that is divisible by both x(16) and y(64) without any remainder.

Methods to Find LCM of 16 and 64

The methods to find the LCM of 16 and 64 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 16 and 64 by Prime Factorization

Prime factorization of 16 and 64 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ respectively. LCM of 16 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ = 64.
Hence, the LCM of 16 and 64 by prime factorization is 64.

LCM of 16 and 64 by Listing Multiples

To calculate the LCM of 16 and 64 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 16 (16, 32, 48, 64, 80, 96, 112, . . . ) and 64 (64, 128, 192, 256, 320, . . . . )
Step 2: The common multiples from the multiples of 16 and 64 are 64, 128, . . .
Step 3: The smallest common multiple of 16 and 64 is 64.

∴ The least common multiple of 16 and 64 = 64.

LCM of 16 and 64 by Division Method

To calculate the LCM of 16 and 64 by the division method, we will divide the numbers(16, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 64.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 64. Write this prime number(2) on the left of the given numbers(16 and 64), separated as per the ladder arrangement.
Step 2: If any of the given numbers (16, 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 16 and 64 is the product of all prime numbers on the left, i.e. LCM(16, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 = 64.

☛ Also Check:

LCM of 16 and 64 Examples

Example 1: The product of two numbers is 1024. If their GCD is 16, what is their LCM?

Solution:

Given: GCD = 16
product of numbers = 1024
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1024/16
Therefore, the LCM is 64.
The probable combination for the given case is LCM(16, 64) = 64.
Example 2: Verify the relationship between GCF and LCM of 16 and 64.

Solution:

The relation between GCF and LCM of 16 and 64 is given as,
LCM(16, 64) × GCF(16, 64) = Product of 16, 64
Prime factorization of 16 and 64 is given as, 16 = (2 × 2 × 2 × 2) = 2⁴ and 64 = (2 × 2 × 2 × 2 × 2 × 2) = 2⁶
LCM(16, 64) = 64
GCF(16, 64) = 16
LHS = LCM(16, 64) × GCF(16, 64) = 64 × 16 = 1024
RHS = Product of 16, 64 = 16 × 64 = 1024
⇒ LHS = RHS = 1024
Hence, verified.
Example 3: The GCD and LCM of two numbers are 16 and 64 respectively. If one number is 16, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 16 × a
⇒ a = (GCD × LCM)/16
⇒ a = (16 × 64)/16
⇒ a = 64
Therefore, the other number is 64.

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FAQs on LCM of 16 and 64

What is the LCM of 16 and 64?

The LCM of 16 and 64 is 64. To find the least common multiple (LCM) of 16 and 64, we need to find the multiples of 16 and 64 (multiples of 16 = 16, 32, 48, 64; multiples of 64 = 64, 128, 192, 256) and choose the smallest multiple that is exactly divisible by 16 and 64, i.e., 64.

If the LCM of 64 and 16 is 64, Find its GCF.

LCM(64, 16) × GCF(64, 16) = 64 × 16
Since the LCM of 64 and 16 = 64
⇒ 64 × GCF(64, 16) = 1024
Therefore, the GCF = 1024/64 = 16.

What is the Least Perfect Square Divisible by 16 and 64?

The least number divisible by 16 and 64 = LCM(16, 64)
LCM of 16 and 64 = 2 × 2 × 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 16 and 64 = 64 [Square root of 64 = √64 = ±8]
Therefore, 64 is the required number.

How to Find the LCM of 16 and 64 by Prime Factorization?

To find the LCM of 16 and 64 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (64 = 2 × 2 × 2 × 2 × 2 × 2). LCM of 16 and 64 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 64.
⇒ LCM of 16, 64 = 2⁶ = 64.

What is the Relation Between GCF and LCM of 16, 64?

The following equation can be used to express the relation between GCF and LCM of 16 and 64, i.e. GCF × LCM = 16 × 64.

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