Least Common Multiple of 52 and 72

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 72 the smallest integer that is 936 that is divisible by both numbers.

Least Common Multiple (LCM) of 52 and 72 is 936.

LCM(52,72) = 936

LCM of 52 and 72

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

LCM of:
and

Least Common Multiple of 52 and 72

LCM of 52 and 72 is 936

Least common multiple can be found by multiplying the highest exponent prime factors of 52 and 72. First we will calculate the prime factors of 52 and 72.

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 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

Now multiplying the highest exponent prime factors to calculate the LCM of 52 and 72.

LCM(52,72) = 23×32×131
LCM(52,72) = 936

Factors of 52

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

1, 2, 4, 13, 26, 52

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Least Common Multiple of 52 and 72 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 72, than apply into the LCM equation.

GCF(52,72) = 4
LCM(52,72) = ( 52 × 72) / 4
LCM(52,72) = 3744 / 4
LCM(52,72) = 936

Properties of LCM 52 and 72

(i) The LCM of 72 and 52 is associative

LCM of 52 and 72 = LCM of 72 and 52

Related Least Common Multiples of 52

Related Least Common Multiples of 72

Frequently Asked Questions on LCM of 52 and 72

1. What is the LCM of 52 and 72?

Answer: LCM of 52 and 72 is 936.

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 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

4. How to Find the LCM of 52 and 72?

Answer:

Least Common Multiple of 52 and 72 = 936

Step 1: Find the prime factorization of 52

52 = 2 x 2 x 13

Step 2: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

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

LCM = 936 = 2 x 2 x 2 x 3 x 3 x 13

Step 4: Therefore, the least common multiple of 52 and 72 is 936.