LCM of 25 and 65

LCM of 25 and 65 is the smallest number among all common multiples of 25 and 65. The first few multiples of 25 and 65 are (25, 50, 75, 100, . . . ) and (65, 130, 195, 260, 325, 390, 455, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 65 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 25 and 65 is 325.

Explanation:

The LCM of two non-zero integers, x(25) and y(65), is the smallest positive integer m(325) that is divisible by both x(25) and y(65) without any remainder.

The methods to find the LCM of 25 and 65 are explained below.

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

LCM of 25 and 65 by Prime Factorization

Prime factorization of 25 and 65 is (5 × 5) = 5² and (5 × 13) = 5¹ × 13¹ respectively. LCM of 25 and 65 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 5² × 13¹ = 325.
Hence, the LCM of 25 and 65 by prime factorization is 325.

LCM of 25 and 65 by Division Method

To calculate the LCM of 25 and 65 by the division method, we will divide the numbers(25, 65) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 65.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 65. Write this prime number(5) on the left of the given numbers(25 and 65), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (25, 65) 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 25 and 65 is the product of all prime numbers on the left, i.e. LCM(25, 65) by division method = 5 × 5 × 13 = 325.

LCM of 25 and 65 by Listing Multiples

To calculate the LCM of 25 and 65 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 65 (65, 130, 195, 260, 325, 390, 455, . . . . )
• Step 2: The common multiples from the multiples of 25 and 65 are 325, 650, . . .
• Step 3: The smallest common multiple of 25 and 65 is 325.

∴ The least common multiple of 25 and 65 = 325.

☛ Also Check:

• LCM of 75 and 105 - 525
• LCM of 36 and 81 - 324
• LCM of 6, 9 and 15 - 90
• LCM of 54 and 27 - 54
• LCM of 18 and 45 - 90
• LCM of 7 and 16 - 112
• LCM of 2, 4 and 7 - 28

FAQs on LCM of 25 and 65

What is the LCM of 25 and 65?

The LCM of 25 and 65 is 325. To find the least common multiple (LCM) of 25 and 65, we need to find the multiples of 25 and 65 (multiples of 25 = 25, 50, 75, 100 . . . . 325; multiples of 65 = 65, 130, 195, 260 . . . . 325) and choose the smallest multiple that is exactly divisible by 25 and 65, i.e., 325.

What are the Methods to Find LCM of 25 and 65?

The commonly used methods to find the LCM of 25 and 65 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

If the LCM of 65 and 25 is 325, Find its GCF.

LCM(65, 25) × GCF(65, 25) = 65 × 25
Since the LCM of 65 and 25 = 325
⇒ 325 × GCF(65, 25) = 1625
Therefore, the greatest common factor (GCF) = 1625/325 = 5.

What is the Relation Between GCF and LCM of 25, 65?

The following equation can be used to express the relation between GCF and LCM of 25 and 65, i.e. GCF × LCM = 25 × 65.

How to Find the LCM of 25 and 65 by Prime Factorization?

To find the LCM of 25 and 65 using prime factorization, we will find the prime factors, (25 = 5 × 5) and (65 = 5 × 13). LCM of 25 and 65 is the product of prime factors raised to their respective highest exponent among the numbers 25 and 65.
⇒ LCM of 25, 65 = 5² × 13¹ = 325.