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LCM of 25 and 16

LCM of 25 and 16 is the smallest number among all common multiples of 25 and 16. The first few multiples of 25 and 16 are (25, 50, 75, 100, 125, 150, . . . ) and (16, 32, 48, 64, 80, 96, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 16 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 25 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 25 and 16?

Answer: LCM of 25 and 16 is 400.

Explanation:

The LCM of two non-zero integers, x(25) and y(16), is the smallest positive integer m(400) that is divisible by both x(25) and y(16) without any remainder.

Methods to Find LCM of 25 and 16

The methods to find the LCM of 25 and 16 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 25 and 16 by Division Method

To calculate the LCM of 25 and 16 by the division method, we will divide the numbers(25, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 16.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 16. Write this prime number(2) on the left of the given numbers(25 and 16), separated as per the ladder arrangement.
Step 2: If any of the given numbers (25, 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 25 and 16 is the product of all prime numbers on the left, i.e. LCM(25, 16) by division method = 2 × 2 × 2 × 2 × 5 × 5 = 400.

LCM of 25 and 16 by Listing Multiples

To calculate the LCM of 25 and 16 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 25 (25, 50, 75, 100, 125, 150, . . . ) and 16 (16, 32, 48, 64, 80, 96, . . . . )
Step 2: The common multiples from the multiples of 25 and 16 are 400, 800, . . .
Step 3: The smallest common multiple of 25 and 16 is 400.

∴ The least common multiple of 25 and 16 = 400.

LCM of 25 and 16 by Prime Factorization

Prime factorization of 25 and 16 is (5 × 5) = 5² and (2 × 2 × 2 × 2) = 2⁴ respectively. LCM of 25 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 5² = 400.
Hence, the LCM of 25 and 16 by prime factorization is 400.

☛ Also Check:

LCM of 25 and 16 Examples

Example 1: Verify the relationship between GCF and LCM of 25 and 16.

Solution:

The relation between GCF and LCM of 25 and 16 is given as,
LCM(25, 16) × GCF(25, 16) = Product of 25, 16
Prime factorization of 25 and 16 is given as, 25 = (5 × 5) = 5² and 16 = (2 × 2 × 2 × 2) = 2⁴
LCM(25, 16) = 400
GCF(25, 16) = 1
LHS = LCM(25, 16) × GCF(25, 16) = 400 × 1 = 400
RHS = Product of 25, 16 = 25 × 16 = 400
⇒ LHS = RHS = 400
Hence, verified.
Example 2: The product of two numbers is 400. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 400
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 400/1
Therefore, the LCM is 400.
The probable combination for the given case is LCM(25, 16) = 400.
Example 3: The GCD and LCM of two numbers are 1 and 400 respectively. If one number is 16, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 16 × b
⇒ b = (GCD × LCM)/16
⇒ b = (1 × 400)/16
⇒ b = 25
Therefore, the other number is 25.

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FAQs on LCM of 25 and 16

What is the LCM of 25 and 16?

The LCM of 25 and 16 is 400. To find the LCM of 25 and 16, we need to find the multiples of 25 and 16 (multiples of 25 = 25, 50, 75, 100 . . . . 400; multiples of 16 = 16, 32, 48, 64 . . . . 400) and choose the smallest multiple that is exactly divisible by 25 and 16, i.e., 400.

What is the Least Perfect Square Divisible by 25 and 16?

The least number divisible by 25 and 16 = LCM(25, 16)
LCM of 25 and 16 = 2 × 2 × 2 × 2 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 25 and 16 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

Which of the following is the LCM of 25 and 16? 400, 2, 12, 42

The value of LCM of 25, 16 is the smallest common multiple of 25 and 16. The number satisfying the given condition is 400.

If the LCM of 16 and 25 is 400, Find its GCF.

LCM(16, 25) × GCF(16, 25) = 16 × 25
Since the LCM of 16 and 25 = 400
⇒ 400 × GCF(16, 25) = 400
Therefore, the greatest common factor (GCF) = 400/400 = 1.

What are the Methods to Find LCM of 25 and 16?

The commonly used methods to find the LCM of 25 and 16 are:

Listing Multiples
Division Method
Prime Factorization Method

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