Least Common Multiple of 168 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 168 and 180 the smallest integer that is 2520 that is divisible by both numbers.

Least Common Multiple (LCM) of 168 and 180 is 2520.

LCM(168,180) = 2520

LCM of 168 and 180

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

LCM of:
and

Least Common Multiple of 168 and 180

LCM of 168 and 180 is 2520

Least common multiple can be found by multiplying the highest exponent prime factors of 168 and 180. First we will calculate the prime factors of 168 and 180.

Prime Factorization of 168


2 168
2 84
2 42
3 21
7 7
1

Prime factors of 168 are 2, 3,7. Prime factorization of 168 in exponential form is:

168 = 23×31×71

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 168 and 180.

LCM(168,180) = 23×32×51×71
LCM(168,180) = 2520

Factors of 168

List of positive integer factors of 168 that divides 168 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

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 168 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 168 and 180, than apply into the LCM equation.

GCF(168,180) = 12
LCM(168,180) = ( 168 × 180) / 12
LCM(168,180) = 30240 / 12
LCM(168,180) = 2520

Properties of LCM 168 and 180

(i) The LCM of 180 and 168 is associative

LCM of 168 and 180 = LCM of 180 and 168

Related Least Common Multiples of 168

Related Least Common Multiples of 180

Frequently Asked Questions on LCM of 168 and 180

1. What is the LCM of 168 and 180?

Answer: LCM of 168 and 180 is 2520.

2. What are the Factors of 168?

Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.

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 168 and 180?

Answer:

Least Common Multiple of 168 and 180 = 2520

Step 1: Find the prime factorization of 168

168 = 2 x 2 x 2 x 3 x 7

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 = 2520 = 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 168 and 180 is 2520.