Least Common Multiple of 52 and 60

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 60 the smallest integer that is 780 that is divisible by both numbers.

Least Common Multiple (LCM) of 52 and 60 is 780.

LCM(52,60) = 780

LCM of 52 and 60

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

LCM of:
and

Least Common Multiple of 52 and 60

LCM of 52 and 60 is 780

Least common multiple can be found by multiplying the highest exponent prime factors of 52 and 60. First we will calculate the prime factors of 52 and 60.

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 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 52 and 60.

LCM(52,60) = 22×31×51×131
LCM(52,60) = 780

Factors of 52

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

1, 2, 4, 13, 26, 52

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Least Common Multiple of 52 and 60 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 60, than apply into the LCM equation.

GCF(52,60) = 4
LCM(52,60) = ( 52 × 60) / 4
LCM(52,60) = 3120 / 4
LCM(52,60) = 780

Properties of LCM 52 and 60

(i) The LCM of 60 and 52 is associative

LCM of 52 and 60 = LCM of 60 and 52

Related Least Common Multiples of 52

Related Least Common Multiples of 60

Frequently Asked Questions on LCM of 52 and 60

1. What is the LCM of 52 and 60?

Answer: LCM of 52 and 60 is 780.

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 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

4. How to Find the LCM of 52 and 60?

Answer:

Least Common Multiple of 52 and 60 = 780

Step 1: Find the prime factorization of 52

52 = 2 x 2 x 13

Step 2: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

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

LCM = 780 = 2 x 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 52 and 60 is 780.