Least Common Multiple of 180 and 186

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 186 the smallest integer that is 5580 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 186 is 5580.

LCM(180,186) = 5580

LCM of 180 and 186

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

LCM of:
and

Least Common Multiple of 180 and 186

LCM of 180 and 186 is 5580

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 186. First we will calculate the prime factors of 180 and 186.

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 186


2 186
3 93
31 31
1

Prime factors of 186 are 2, 3,31. Prime factorization of 186 in exponential form is:

186 = 21×31×311

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 186.

LCM(180,186) = 22×32×51×311
LCM(180,186) = 5580

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 186

List of positive integer factors of 186 that divides 186 without a remainder.

1, 2, 3, 6, 31, 62, 93, 186

Least Common Multiple of 180 and 186 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 186, than apply into the LCM equation.

GCF(180,186) = 6
LCM(180,186) = ( 180 × 186) / 6
LCM(180,186) = 33480 / 6
LCM(180,186) = 5580

Properties of LCM 180 and 186

(i) The LCM of 186 and 180 is associative

LCM of 180 and 186 = LCM of 186 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 186

Frequently Asked Questions on LCM of 180 and 186

1. What is the LCM of 180 and 186?

Answer: LCM of 180 and 186 is 5580.

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 186?

Answer: Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186. There are 8 integers that are factors of 186. The greatest factor of 186 is 186.

4. How to Find the LCM of 180 and 186?

Answer:

Least Common Multiple of 180 and 186 = 5580

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 186

186 = 2 x 3 x 31

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

LCM = 5580 = 2 x 2 x 3 x 3 x 5 x 31

Step 4: Therefore, the least common multiple of 180 and 186 is 5580.