Least Common Multiple of 30 and 36

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 30 and 36 the smallest integer that is 180 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 36 is 180.

LCM(30,36) = 180

LCM of 30 and 36

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

LCM of:
and

Least Common Multiple of 30 and 36

LCM of 30 and 36 is 180

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 36. First we will calculate the prime factors of 30 and 36.

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 36.

LCM(30,36) = 22×32×51
LCM(30,36) = 180

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

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

Least Common Multiple of 30 and 36 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 36, than apply into the LCM equation.

GCF(30,36) = 6
LCM(30,36) = ( 30 × 36) / 6
LCM(30,36) = 1080 / 6
LCM(30,36) = 180

Properties of LCM 30 and 36

(i) The LCM of 36 and 30 is associative

LCM of 30 and 36 = LCM of 36 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 36

Frequently Asked Questions on LCM of 30 and 36

1. What is the LCM of 30 and 36?

Answer: LCM of 30 and 36 is 180.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

3. 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.

4. How to Find the LCM of 30 and 36?

Answer:

Least Common Multiple of 30 and 36 = 180

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 36

36 = 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 = 180 = 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 30 and 36 is 180.