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LCM of 15 and 25

LCM of 15 and 25 is the smallest number among all common multiples of 15 and 25. The first few multiples of 15 and 25 are (15, 30, 45, 60, 75, . . . ) and (25, 50, 75, 100, 125, 150, 175, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 25 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 15 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 15 and 25?

Answer: LCM of 15 and 25 is 75.

Explanation:

The LCM of two non-zero integers, x(15) and y(25), is the smallest positive integer m(75) that is divisible by both x(15) and y(25) without any remainder.

Methods to Find LCM of 15 and 25

The methods to find the LCM of 15 and 25 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 15 and 25 by Prime Factorization

Prime factorization of 15 and 25 is (3 × 5) = 3¹ × 5¹ and (5 × 5) = 5² respectively. LCM of 15 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5² = 75.
Hence, the LCM of 15 and 25 by prime factorization is 75.

LCM of 15 and 25 by Listing Multiples

To calculate the LCM of 15 and 25 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, . . . ) and 25 (25, 50, 75, 100, 125, 150, 175, . . . . )
Step 2: The common multiples from the multiples of 15 and 25 are 75, 150, . . .
Step 3: The smallest common multiple of 15 and 25 is 75.

∴ The least common multiple of 15 and 25 = 75.

LCM of 15 and 25 by Division Method

To calculate the LCM of 15 and 25 by the division method, we will divide the numbers(15, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 25.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 25. Write this prime number(3) on the left of the given numbers(15 and 25), separated as per the ladder arrangement.
Step 2: If any of the given numbers (15, 25) is a multiple of 3, divide it by 3 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 15 and 25 is the product of all prime numbers on the left, i.e. LCM(15, 25) by division method = 3 × 5 × 5 = 75.

☛ Also Check:

LCM of 15 and 25 Examples

Example 1: Find the smallest number that is divisible by 15 and 25 exactly.

Solution:

The smallest number that is divisible by 15 and 25 exactly is their LCM.
⇒ Multiples of 15 and 25:
- Multiples of 15 = 15, 30, 45, 60, 75, . . . .
- Multiples of 25 = 25, 50, 75, 100, 125, . . . .
Therefore, the LCM of 15 and 25 is 75.
Example 2: Verify the relationship between GCF and LCM of 15 and 25.

Solution:

The relation between GCF and LCM of 15 and 25 is given as,
LCM(15, 25) × GCF(15, 25) = Product of 15, 25
Prime factorization of 15 and 25 is given as, 15 = (3 × 5) = 3¹ × 5¹ and 25 = (5 × 5) = 5²
LCM(15, 25) = 75
GCF(15, 25) = 5
LHS = LCM(15, 25) × GCF(15, 25) = 75 × 5 = 375
RHS = Product of 15, 25 = 15 × 25 = 375
⇒ LHS = RHS = 375
Hence, verified.
Example 3: The product of two numbers is 375. If their GCD is 5, what is their LCM?

Solution:

Given: GCD = 5
product of numbers = 375
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 375/5
Therefore, the LCM is 75.
The probable combination for the given case is LCM(15, 25) = 75.

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FAQs on LCM of 15 and 25

What is the LCM of 15 and 25?

The LCM of 15 and 25 is 75. To find the LCM of 15 and 25, we need to find the multiples of 15 and 25 (multiples of 15 = 15, 30, 45, 60 . . . . 75; multiples of 25 = 25, 50, 75, 100) and choose the smallest multiple that is exactly divisible by 15 and 25, i.e., 75.

Which of the following is the LCM of 15 and 25? 28, 12, 75, 30

The value of LCM of 15, 25 is the smallest common multiple of 15 and 25. The number satisfying the given condition is 75.

If the LCM of 25 and 15 is 75, Find its GCF.

LCM(25, 15) × GCF(25, 15) = 25 × 15
Since the LCM of 25 and 15 = 75
⇒ 75 × GCF(25, 15) = 375
Therefore, the GCF (greatest common factor) = 375/75 = 5.

How to Find the LCM of 15 and 25 by Prime Factorization?

To find the LCM of 15 and 25 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (25 = 5 × 5). LCM of 15 and 25 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 25.
⇒ LCM of 15, 25 = 3¹ × 5² = 75.

What is the Least Perfect Square Divisible by 15 and 25?

The least number divisible by 15 and 25 = LCM(15, 25)
LCM of 15 and 25 = 3 × 5 × 5 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 15 and 25 = LCM(15, 25) × 3 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.

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