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LCM of 5 and 25

LCM of 5 and 25 is the smallest number among all common multiples of 5 and 25. The first few multiples of 5 and 25 are (5, 10, 15, 20, 25, 30, . . . ) and (25, 50, 75, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 25 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 5 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 5 and 25?

Answer: LCM of 5 and 25 is 25.

Explanation:

The LCM of two non-zero integers, x(5) and y(25), is the smallest positive integer m(25) that is divisible by both x(5) and y(25) without any remainder.

Methods to Find LCM of 5 and 25

Let's look at the different methods for finding the LCM of 5 and 25.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 5 and 25 by Division Method

To calculate the LCM of 5 and 25 by the division method, we will divide the numbers(5, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 25.

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

LCM of 5 and 25 by Prime Factorization

Prime factorization of 5 and 25 is (5) = 5¹ and (5 × 5) = 5² respectively. LCM of 5 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 5² = 25.
Hence, the LCM of 5 and 25 by prime factorization is 25.

LCM of 5 and 25 by Listing Multiples

To calculate the LCM of 5 and 25 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 25 (25, 50, 75, 100, . . . . )
Step 2: The common multiples from the multiples of 5 and 25 are 25, 50, . . .
Step 3: The smallest common multiple of 5 and 25 is 25.

∴ The least common multiple of 5 and 25 = 25.

☛ Also Check:

LCM of 5 and 25 Examples

Example 1: Verify the relationship between GCF and LCM of 5 and 25.

Solution:

The relation between GCF and LCM of 5 and 25 is given as,
LCM(5, 25) × GCF(5, 25) = Product of 5, 25
Prime factorization of 5 and 25 is given as, 5 = (5) = 5¹ and 25 = (5 × 5) = 5²
LCM(5, 25) = 25
GCF(5, 25) = 5
LHS = LCM(5, 25) × GCF(5, 25) = 25 × 5 = 125
RHS = Product of 5, 25 = 5 × 25 = 125
⇒ LHS = RHS = 125
Hence, verified.
Example 2: The product of two numbers is 125. If their GCD is 5, what is their LCM?

Solution:

Given: GCD = 5
product of numbers = 125
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 125/5
Therefore, the LCM is 25.
The probable combination for the given case is LCM(5, 25) = 25.
Example 3: The GCD and LCM of two numbers are 5 and 25 respectively. If one number is 25, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 25 × a
⇒ a = (GCD × LCM)/25
⇒ a = (5 × 25)/25
⇒ a = 5
Therefore, the other number is 5.

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FAQs on LCM of 5 and 25

What is the LCM of 5 and 25?

The LCM of 5 and 25 is 25. To find the least common multiple (LCM) of 5 and 25, we need to find the multiples of 5 and 25 (multiples of 5 = 5, 10, 15, 20 . . . . 25; multiples of 25 = 25, 50, 75, 100) and choose the smallest multiple that is exactly divisible by 5 and 25, i.e., 25.

What is the Least Perfect Square Divisible by 5 and 25?

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

What is the Relation Between GCF and LCM of 5, 25?

The following equation can be used to express the relation between GCF and LCM of 5 and 25, i.e. GCF × LCM = 5 × 25.

How to Find the LCM of 5 and 25 by Prime Factorization?

To find the LCM of 5 and 25 using prime factorization, we will find the prime factors, (5 = 5) and (25 = 5 × 5). LCM of 5 and 25 is the product of prime factors raised to their respective highest exponent among the numbers 5 and 25.
⇒ LCM of 5, 25 = 5² = 25.

If the LCM of 25 and 5 is 25, Find its GCF.

LCM(25, 5) × GCF(25, 5) = 25 × 5
Since the LCM of 25 and 5 = 25
⇒ 25 × GCF(25, 5) = 125
Therefore, the greatest common factor (GCF) = 125/25 = 5.

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