Least Common Multiple of 180 and 188

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 180 and 188 the smallest integer that is 8460 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 188 is 8460.

LCM(180,188) = 8460

LCM of 180 and 188

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

LCM of:
and

Least Common Multiple of 180 and 188

LCM of 180 and 188 is 8460

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 188. First we will calculate the prime factors of 180 and 188.

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

Prime Factorization of 188


2 188
2 94
47 47
1

Prime factors of 188 are 2,47. Prime factorization of 188 in exponential form is:

188 = 22×471

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 188.

LCM(180,188) = 22×32×51×471
LCM(180,188) = 8460

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

Factors of 188

List of positive integer factors of 188 that divides 188 without a remainder.

1, 2, 4, 47, 94, 188

Least Common Multiple of 180 and 188 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 180 and 188, than apply into the LCM equation.

GCF(180,188) = 4
LCM(180,188) = ( 180 × 188) / 4
LCM(180,188) = 33840 / 4
LCM(180,188) = 8460

Properties of LCM 180 and 188

(i) The LCM of 188 and 180 is associative

LCM of 180 and 188 = LCM of 188 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 188

Frequently Asked Questions on LCM of 180 and 188

1. What is the LCM of 180 and 188?

Answer: LCM of 180 and 188 is 8460.

2. 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.

3. What are the Factors of 188?

Answer: Factors of 188 are 1, 2, 4, 47, 94, 188. There are 6 integers that are factors of 188. The greatest factor of 188 is 188.

4. How to Find the LCM of 180 and 188?

Answer:

Least Common Multiple of 180 and 188 = 8460

Step 1: Find the prime factorization of 180

180 = 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 188

188 = 2 x 2 x 47

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 8460 = 2 x 2 x 3 x 3 x 5 x 47

Step 4: Therefore, the least common multiple of 180 and 188 is 8460.