LCM of 25 and 50

LCM of 25 and 50 is the smallest number among all common multiples of 25 and 50. The first few multiples of 25 and 50 are (25, 50, 75, 100, 125, 150, . . . ) and (50, 100, 150, 200, 250, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 50 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 25 and 50 is 50.

Explanation:

The LCM of two non-zero integers, x(25) and y(50), is the smallest positive integer m(50) that is divisible by both x(25) and y(50) without any remainder.

The methods to find the LCM of 25 and 50 are explained below.

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

LCM of 25 and 50 by Division Method

To calculate the LCM of 25 and 50 by the division method, we will divide the numbers(25, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 50.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 50. Write this prime number(2) on the left of the given numbers(25 and 50), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (25, 50) 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 50 is the product of all prime numbers on the left, i.e. LCM(25, 50) by division method = 2 × 5 × 5 = 50.

LCM of 25 and 50 by Listing Multiples

To calculate the LCM of 25 and 50 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 50 (50, 100, 150, 200, 250, 300, . . . . )
• Step 2: The common multiples from the multiples of 25 and 50 are 50, 100, . . .
• Step 3: The smallest common multiple of 25 and 50 is 50.

∴ The least common multiple of 25 and 50 = 50.

LCM of 25 and 50 by Prime Factorization

Prime factorization of 25 and 50 is (5 × 5) = 5² and (2 × 5 × 5) = 2¹ × 5² respectively. LCM of 25 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5² = 50.
Hence, the LCM of 25 and 50 by prime factorization is 50.

☛ Also Check:

• LCM of 15 and 60 - 60
• LCM of 12, 24 and 36 - 72
• LCM of 8 and 28 - 56
• LCM of 20 and 45 - 180
• LCM of 12, 15 and 21 - 420
• LCM of 5 and 16 - 80
• LCM of 9 and 13 - 117

FAQs on LCM of 25 and 50

What is the LCM of 25 and 50?

The LCM of 25 and 50 is 50. To find the least common multiple of 25 and 50, we need to find the multiples of 25 and 50 (multiples of 25 = 25, 50, 75, 100; multiples of 50 = 50, 100, 150, 200) and choose the smallest multiple that is exactly divisible by 25 and 50, i.e., 50.

If the LCM of 50 and 25 is 50, Find its GCF.

LCM(50, 25) × GCF(50, 25) = 50 × 25
Since the LCM of 50 and 25 = 50
⇒ 50 × GCF(50, 25) = 1250
Therefore, the GCF (greatest common factor) = 1250/50 = 25.

What are the Methods to Find LCM of 25 and 50?

The commonly used methods to find the LCM of 25 and 50 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

What is the Least Perfect Square Divisible by 25 and 50?

The least number divisible by 25 and 50 = LCM(25, 50)
LCM of 25 and 50 = 2 × 5 × 5 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 25 and 50 = LCM(25, 50) × 2 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.

What is the Relation Between GCF and LCM of 25, 50?

The following equation can be used to express the relation between GCF and LCM of 25 and 50, i.e. GCF × LCM = 25 × 50.