Least Common Multiple of 36 and 52

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 36 and 52 the smallest integer that is 468 that is divisible by both numbers.

Least Common Multiple (LCM) of 36 and 52 is 468.

LCM(36,52) = 468

LCM of 36 and 52

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

LCM of:
and

Least Common Multiple of 36 and 52

LCM of 36 and 52 is 468

Least common multiple can be found by multiplying the highest exponent prime factors of 36 and 52. First we will calculate the prime factors of 36 and 52.

Prime Factorization of 36


2 36
2 18
3 9
3 3
1

Prime factors of 36 are 2,3. Prime factorization of 36 in exponential form is:

36 = 22×32

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

Now multiplying the highest exponent prime factors to calculate the LCM of 36 and 52.

LCM(36,52) = 22×32×131
LCM(36,52) = 468

Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 52

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

1, 2, 4, 13, 26, 52

Least Common Multiple of 36 and 52 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36 and 52, than apply into the LCM equation.

GCF(36,52) = 4
LCM(36,52) = ( 36 × 52) / 4
LCM(36,52) = 1872 / 4
LCM(36,52) = 468

Properties of LCM 36 and 52

(i) The LCM of 52 and 36 is associative

LCM of 36 and 52 = LCM of 52 and 36

Related Least Common Multiples of 36

Related Least Common Multiples of 52

Frequently Asked Questions on LCM of 36 and 52

1. What is the LCM of 36 and 52?

Answer: LCM of 36 and 52 is 468.

2. What are the Factors of 36?

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

3. 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.

4. How to Find the LCM of 36 and 52?

Answer:

Least Common Multiple of 36 and 52 = 468

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 52

52 = 2 x 2 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 = 468 = 2 x 2 x 3 x 3 x 13

Step 4: Therefore, the least common multiple of 36 and 52 is 468.