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LCM of 4 and 16

LCM of 4 and 16 is the smallest number among all common multiples of 4 and 16. The first few multiples of 4 and 16 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (16, 32, 48, 64, 80, 96, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 16 - by listing multiples, by division method, and by prime factorization.

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

What is the LCM of 4 and 16?

Answer: LCM of 4 and 16 is 16.

Explanation:

The LCM of two non-zero integers, x(4) and y(16), is the smallest positive integer m(16) that is divisible by both x(4) and y(16) without any remainder.

Methods to Find LCM of 4 and 16

Let's look at the different methods for finding the LCM of 4 and 16.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 4 and 16 by Listing Multiples

To calculate the LCM of 4 and 16 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, 28, . . . ) and 16 (16, 32, 48, 64, 80, 96, . . . . )
Step 2: The common multiples from the multiples of 4 and 16 are 16, 32, . . .
Step 3: The smallest common multiple of 4 and 16 is 16.

∴ The least common multiple of 4 and 16 = 16.

LCM of 4 and 16 by Prime Factorization

Prime factorization of 4 and 16 is (2 × 2) = 2² and (2 × 2 × 2 × 2) = 2⁴ respectively. LCM of 4 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ = 16.
Hence, the LCM of 4 and 16 by prime factorization is 16.

LCM of 4 and 16 by Division Method

To calculate the LCM of 4 and 16 by the division method, we will divide the numbers(4, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 16.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 16. Write this prime number(2) on the left of the given numbers(4 and 16), separated as per the ladder arrangement.
Step 2: If any of the given numbers (4, 16) 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 4 and 16 is the product of all prime numbers on the left, i.e. LCM(4, 16) by division method = 2 × 2 × 2 × 2 = 16.

☛ Also Check:

LCM of 4 and 16 Examples

Example 1: The product of two numbers is 64. If their GCD is 4, what is their LCM?

Solution:

Given: GCD = 4
product of numbers = 64
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 64/4
Therefore, the LCM is 16.
The probable combination for the given case is LCM(4, 16) = 16.
Example 2: The GCD and LCM of two numbers are 4 and 16 respectively. If one number is 16, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 16 × p
⇒ p = (GCD × LCM)/16
⇒ p = (4 × 16)/16
⇒ p = 4
Therefore, the other number is 4.
Example 3: Find the smallest number that is divisible by 4 and 16 exactly.

Solution:

The smallest number that is divisible by 4 and 16 exactly is their LCM.
⇒ Multiples of 4 and 16:
- Multiples of 4 = 4, 8, 12, 16, 20, . . . .
- Multiples of 16 = 16, 32, 48, 64, 80, . . . .
Therefore, the LCM of 4 and 16 is 16.

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FAQs on LCM of 4 and 16

What is the LCM of 4 and 16?

The LCM of 4 and 16 is 16. To find the least common multiple (LCM) of 4 and 16, we need to find the multiples of 4 and 16 (multiples of 4 = 4, 8, 12, 16; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 4 and 16, i.e., 16.

How to Find the LCM of 4 and 16 by Prime Factorization?

To find the LCM of 4 and 16 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (16 = 2 × 2 × 2 × 2). LCM of 4 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 16.
⇒ LCM of 4, 16 = 2⁴ = 16.

What is the Least Perfect Square Divisible by 4 and 16?

The least number divisible by 4 and 16 = LCM(4, 16)
LCM of 4 and 16 = 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 4 and 16 = 16 [Square root of 16 = √16 = ±4]
Therefore, 16 is the required number.

If the LCM of 16 and 4 is 16, Find its GCF.

LCM(16, 4) × GCF(16, 4) = 16 × 4
Since the LCM of 16 and 4 = 16
⇒ 16 × GCF(16, 4) = 64
Therefore, the greatest common factor (GCF) = 64/16 = 4.

What is the Relation Between GCF and LCM of 4, 16?

The following equation can be used to express the relation between GCF and LCM of 4 and 16, i.e. GCF × LCM = 4 × 16.

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