LCM of 6 and 25

LCM of 6 and 25 is the smallest number among all common multiples of 6 and 25. The first few multiples of 6 and 25 are (6, 12, 18, 24, 30, . . . ) and (25, 50, 75, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 25 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 6 and 25 is 150.

Explanation:

The LCM of two non-zero integers, x(6) and y(25), is the smallest positive integer m(150) that is divisible by both x(6) and y(25) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 25.

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

LCM of 6 and 25 by Division Method

To calculate the LCM of 6 and 25 by the division method, we will divide the numbers(6, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 25.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 25. Write this prime number(2) on the left of the given numbers(6 and 25), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 25) 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 6 and 25 is the product of all prime numbers on the left, i.e. LCM(6, 25) by division method = 2 × 3 × 5 × 5 = 150.

LCM of 6 and 25 by Prime Factorization

Prime factorization of 6 and 25 is (2 × 3) = 2¹ × 3¹ and (5 × 5) = 5² respectively. LCM of 6 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5² = 150.
Hence, the LCM of 6 and 25 by prime factorization is 150.

LCM of 6 and 25 by Listing Multiples

To calculate the LCM of 6 and 25 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, . . . ) and 25 (25, 50, 75, 100, . . . . )
• Step 2: The common multiples from the multiples of 6 and 25 are 150, 300, . . .
• Step 3: The smallest common multiple of 6 and 25 is 150.

∴ The least common multiple of 6 and 25 = 150.

☛ Also Check:

• LCM of 7 and 21 - 21
• LCM of 16 and 60 - 240
• LCM of 5 and 24 - 120
• LCM of 10 and 18 - 90
• LCM of 6, 12, 18 and 24 - 72
• LCM of 6, 7 and 8 - 168
• LCM of 4, 8 and 12 - 24

FAQs on LCM of 6 and 25

What is the LCM of 6 and 25?

The LCM of 6 and 25 is 150. To find the least common multiple (LCM) of 6 and 25, we need to find the multiples of 6 and 25 (multiples of 6 = 6, 12, 18, 24 . . . . 150; multiples of 25 = 25, 50, 75, 100 . . . . 150) and choose the smallest multiple that is exactly divisible by 6 and 25, i.e., 150.

What is the Relation Between GCF and LCM of 6, 25?

The following equation can be used to express the relation between GCF and LCM of 6 and 25, i.e. GCF × LCM = 6 × 25.

If the LCM of 25 and 6 is 150, Find its GCF.

LCM(25, 6) × GCF(25, 6) = 25 × 6
Since the LCM of 25 and 6 = 150
⇒ 150 × GCF(25, 6) = 150
Therefore, the greatest common factor (GCF) = 150/150 = 1.

What are the Methods to Find LCM of 6 and 25?

The commonly used methods to find the LCM of 6 and 25 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 6 and 25?

The least number divisible by 6 and 25 = LCM(6, 25)
LCM of 6 and 25 = 2 × 3 × 5 × 5 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 6 and 25 = LCM(6, 25) × 2 × 3 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.