LCM of 25 and 75

LCM of 25 and 75 is the smallest number among all common multiples of 25 and 75. The first few multiples of 25 and 75 are (25, 50, 75, 100, . . . ) and (75, 150, 225, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 75 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 25 and 75 is 75.

Explanation:

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

The methods to find the LCM of 25 and 75 are explained below.

• By Listing Multiples
• By Prime Factorization Method
• By Division Method

LCM of 25 and 75 by Listing Multiples

To calculate the LCM of 25 and 75 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, . . . ) and 75 (75, 150, 225, 300, . . . . )
• Step 2: The common multiples from the multiples of 25 and 75 are 75, 150, . . .
• Step 3: The smallest common multiple of 25 and 75 is 75.

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

LCM of 25 and 75 by Prime Factorization

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

LCM of 25 and 75 by Division Method

To calculate the LCM of 25 and 75 by the division method, we will divide the numbers(25, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 75.

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

☛ Also Check:

• LCM of 6, 8 and 12 - 24
• LCM of 3, 4 and 7 - 84
• LCM of 24 and 8 - 24
• LCM of 3, 4 and 6 - 12
• LCM of 60 and 62 - 1860
• LCM of 16, 20 and 24 - 240
• LCM of 21 and 24 - 168

FAQs on LCM of 25 and 75

What is the LCM of 25 and 75?

The LCM of 25 and 75 is 75. To find the LCM (least common multiple) of 25 and 75, we need to find the multiples of 25 and 75 (multiples of 25 = 25, 50, 75, 100; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 25 and 75, i.e., 75.

What is the Least Perfect Square Divisible by 25 and 75?

The least number divisible by 25 and 75 = LCM(25, 75)
LCM of 25 and 75 = 3 × 5 × 5 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 25 and 75 = LCM(25, 75) × 3 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.

What are the Methods to Find LCM of 25 and 75?

The commonly used methods to find the LCM of 25 and 75 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

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

LCM(75, 25) × GCF(75, 25) = 75 × 25
Since the LCM of 75 and 25 = 75
⇒ 75 × GCF(75, 25) = 1875
Therefore, the greatest common factor (GCF) = 1875/75 = 25.

What is the Relation Between GCF and LCM of 25, 75?

The following equation can be used to express the relation between GCF and LCM of 25 and 75, i.e. GCF × LCM = 25 × 75.