Least Common Multiple of 52 and 65

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 52 and 65 the smallest integer that is 260 that is divisible by both numbers.

Least Common Multiple (LCM) of 52 and 65 is 260.

LCM(52,65) = 260

LCM of 52 and 65

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 52 and 65

LCM of 52 and 65 is 260

Least common multiple can be found by multiplying the highest exponent prime factors of 52 and 65. First we will calculate the prime factors of 52 and 65.

Prime Factorization of 52


2 52
2 26
13 13
1

Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:

52 = 22×131

Prime Factorization of 65


5 65
13 13
1

Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:

65 = 51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 52 and 65.

LCM(52,65) = 22×51×131
LCM(52,65) = 260

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1, 2, 4, 13, 26, 52

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1, 5, 13, 65

Least Common Multiple of 52 and 65 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 52 and 65, than apply into the LCM equation.

GCF(52,65) = 13
LCM(52,65) = ( 52 × 65) / 13
LCM(52,65) = 3380 / 13
LCM(52,65) = 260

Properties of LCM 52 and 65

(i) The LCM of 65 and 52 is associative

LCM of 52 and 65 = LCM of 65 and 52

Related Least Common Multiples of 52

Related Least Common Multiples of 65

Frequently Asked Questions on LCM of 52 and 65

1. What is the LCM of 52 and 65?

Answer: LCM of 52 and 65 is 260.

2. What are the Factors of 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

3. What are the Factors of 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

4. How to Find the LCM of 52 and 65?

Answer:

Least Common Multiple of 52 and 65 = 260

Step 1: Find the prime factorization of 52

52 = 2 x 2 x 13

Step 2: Find the prime factorization of 65

65 = 5 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 260 = 2 x 2 x 5 x 13

Step 4: Therefore, the least common multiple of 52 and 65 is 260.