Least Common Multiple of 180 and 185

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 185 the smallest integer that is 6660 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 185 is 6660.

LCM(180,185) = 6660

LCM of 180 and 185

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

LCM of:
and

Least Common Multiple of 180 and 185

LCM of 180 and 185 is 6660

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 185. First we will calculate the prime factors of 180 and 185.

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 185


5 185
37 37
1

Prime factors of 185 are 5,37. Prime factorization of 185 in exponential form is:

185 = 51×371

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 185.

LCM(180,185) = 22×32×51×371
LCM(180,185) = 6660

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 185

List of positive integer factors of 185 that divides 185 without a remainder.

1, 5, 37, 185

Least Common Multiple of 180 and 185 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 185, than apply into the LCM equation.

GCF(180,185) = 5
LCM(180,185) = ( 180 × 185) / 5
LCM(180,185) = 33300 / 5
LCM(180,185) = 6660

Properties of LCM 180 and 185

(i) The LCM of 185 and 180 is associative

LCM of 180 and 185 = LCM of 185 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 185

Frequently Asked Questions on LCM of 180 and 185

1. What is the LCM of 180 and 185?

Answer: LCM of 180 and 185 is 6660.

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 185?

Answer: Factors of 185 are 1, 5, 37, 185. There are 4 integers that are factors of 185. The greatest factor of 185 is 185.

4. How to Find the LCM of 180 and 185?

Answer:

Least Common Multiple of 180 and 185 = 6660

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 185

185 = 5 x 37

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

LCM = 6660 = 2 x 2 x 3 x 3 x 5 x 37

Step 4: Therefore, the least common multiple of 180 and 185 is 6660.