Least Common Multiple of 36 and 39

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 39 the smallest integer that is 468 that is divisible by both numbers.

Least Common Multiple (LCM) of 36 and 39 is 468.

LCM(36,39) = 468

LCM of 36 and 39

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

LCM of:
and

Least Common Multiple of 36 and 39

LCM of 36 and 39 is 468

Least common multiple can be found by multiplying the highest exponent prime factors of 36 and 39. First we will calculate the prime factors of 36 and 39.

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 39


3 39
13 13
1

Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:

39 = 31×131

Now multiplying the highest exponent prime factors to calculate the LCM of 36 and 39.

LCM(36,39) = 22×32×131
LCM(36,39) = 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 39

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13, 39

Least Common Multiple of 36 and 39 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 39, than apply into the LCM equation.

GCF(36,39) = 3
LCM(36,39) = ( 36 × 39) / 3
LCM(36,39) = 1404 / 3
LCM(36,39) = 468

Properties of LCM 36 and 39

(i) The LCM of 39 and 36 is associative

LCM of 36 and 39 = LCM of 39 and 36

Related Least Common Multiples of 36

Related Least Common Multiples of 39

Frequently Asked Questions on LCM of 36 and 39

1. What is the LCM of 36 and 39?

Answer: LCM of 36 and 39 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 39?

Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.

4. How to Find the LCM of 36 and 39?

Answer:

Least Common Multiple of 36 and 39 = 468

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 39

39 = 3 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 39 is 468.