Least Common Multiple of 120 and 180

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 120 and 180 the smallest integer that is 360 that is divisible by both numbers.

Least Common Multiple (LCM) of 120 and 180 is 360.

LCM(120,180) = 360

LCM of 120 and 180

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

LCM of:
and

Least Common Multiple of 120 and 180

LCM of 120 and 180 is 360

Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 180. First we will calculate the prime factors of 120 and 180.

Prime Factorization of 120


2 120
2 60
2 30
3 15
5 5
1

Prime factors of 120 are 2, 3,5. Prime factorization of 120 in exponential form is:

120 = 23×31×51

Prime Factorization of 180


2 180
2 90
3 45
3 15
5 5
1

Prime factors of 180 are 2, 3,5. Prime factorization of 180 in exponential form is:

180 = 22×32×51

Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 180.

LCM(120,180) = 23×32×51
LCM(120,180) = 360

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Least Common Multiple of 120 and 180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 120 and 180, than apply into the LCM equation.

GCF(120,180) = 60
LCM(120,180) = ( 120 × 180) / 60
LCM(120,180) = 21600 / 60
LCM(120,180) = 360

Properties of LCM 120 and 180

(i) The LCM of 180 and 120 is associative

LCM of 120 and 180 = LCM of 180 and 120

Related Least Common Multiples of 120

Related Least Common Multiples of 180

Frequently Asked Questions on LCM of 120 and 180

1. What is the LCM of 120 and 180?

Answer: LCM of 120 and 180 is 360.

2. What are the Factors of 120?

Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.

3. What are the Factors of 180?

Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.

4. How to Find the LCM of 120 and 180?

Answer:

Least Common Multiple of 120 and 180 = 360

Step 1: Find the prime factorization of 120

120 = 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 180

180 = 2 x 2 x 3 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 = 360 = 2 x 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 120 and 180 is 360.