LCM of 39 and 65

LCM of 39 and 65 is the smallest number among all common multiples of 39 and 65. The first few multiples of 39 and 65 are (39, 78, 117, 156, 195, . . . ) and (65, 130, 195, 260, 325, 390, . . . ) respectively. There are 3 commonly used methods to find LCM of 39 and 65 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 39 and 65 is 195.

Explanation:

The LCM of two non-zero integers, x(39) and y(65), is the smallest positive integer m(195) that is divisible by both x(39) and y(65) without any remainder.

The methods to find the LCM of 39 and 65 are explained below.

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

LCM of 39 and 65 by Prime Factorization

Prime factorization of 39 and 65 is (3 × 13) = 3¹ × 13¹ and (5 × 13) = 5¹ × 13¹ respectively. LCM of 39 and 65 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 13¹ = 195.
Hence, the LCM of 39 and 65 by prime factorization is 195.

LCM of 39 and 65 by Division Method

To calculate the LCM of 39 and 65 by the division method, we will divide the numbers(39, 65) by their prime factors (preferably common). The product of these divisors gives the LCM of 39 and 65.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 39 and 65. Write this prime number(3) on the left of the given numbers(39 and 65), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (39, 65) 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 39 and 65 is the product of all prime numbers on the left, i.e. LCM(39, 65) by division method = 3 × 5 × 13 = 195.

LCM of 39 and 65 by Listing Multiples

To calculate the LCM of 39 and 65 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 39 (39, 78, 117, 156, 195, . . . ) and 65 (65, 130, 195, 260, 325, 390, . . . . )
• Step 2: The common multiples from the multiples of 39 and 65 are 195, 390, . . .
• Step 3: The smallest common multiple of 39 and 65 is 195.

∴ The least common multiple of 39 and 65 = 195.

☛ Also Check:

• LCM of 11 and 18 - 198
• LCM of 15 and 20 - 60
• LCM of 8 and 9 - 72
• LCM of 2, 3, 4 and 5 - 60
• LCM of 23 and 69 - 69
• LCM of 15 and 27 - 135
• LCM of 24 and 48 - 48

FAQs on LCM of 39 and 65

What is the LCM of 39 and 65?

The LCM of 39 and 65 is 195. To find the LCM of 39 and 65, we need to find the multiples of 39 and 65 (multiples of 39 = 39, 78, 117, 156 . . . . 195; multiples of 65 = 65, 130, 195, 260) and choose the smallest multiple that is exactly divisible by 39 and 65, i.e., 195.

What are the Methods to Find LCM of 39 and 65?

The commonly used methods to find the LCM of 39 and 65 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

What is the Relation Between GCF and LCM of 39, 65?

The following equation can be used to express the relation between GCF and LCM of 39 and 65, i.e. GCF × LCM = 39 × 65.

If the LCM of 65 and 39 is 195, Find its GCF.

LCM(65, 39) × GCF(65, 39) = 65 × 39
Since the LCM of 65 and 39 = 195
⇒ 195 × GCF(65, 39) = 2535
Therefore, the greatest common factor = 2535/195 = 13.

What is the Least Perfect Square Divisible by 39 and 65?

The least number divisible by 39 and 65 = LCM(39, 65)
LCM of 39 and 65 = 3 × 5 × 13 [Incomplete pair(s): 3, 5, 13]
⇒ Least perfect square divisible by each 39 and 65 = LCM(39, 65) × 3 × 5 × 13 = 38025 [Square root of 38025 = √38025 = ±195]
Therefore, 38025 is the required number.