Least Common Multiple of 180 and 182

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 182 the smallest integer that is 16380 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 182 is 16380.

LCM(180,182) = 16380

LCM of 180 and 182

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

LCM of:
and

Least Common Multiple of 180 and 182

LCM of 180 and 182 is 16380

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 182. First we will calculate the prime factors of 180 and 182.

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 182


2 182
7 91
13 13
1

Prime factors of 182 are 2, 7,13. Prime factorization of 182 in exponential form is:

182 = 21×71×131

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 182.

LCM(180,182) = 22×32×51×71×131
LCM(180,182) = 16380

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 182

List of positive integer factors of 182 that divides 182 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182

Least Common Multiple of 180 and 182 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 182, than apply into the LCM equation.

GCF(180,182) = 2
LCM(180,182) = ( 180 × 182) / 2
LCM(180,182) = 32760 / 2
LCM(180,182) = 16380

Properties of LCM 180 and 182

(i) The LCM of 182 and 180 is associative

LCM of 180 and 182 = LCM of 182 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 182

Frequently Asked Questions on LCM of 180 and 182

1. What is the LCM of 180 and 182?

Answer: LCM of 180 and 182 is 16380.

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 182?

Answer: Factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182. There are 8 integers that are factors of 182. The greatest factor of 182 is 182.

4. How to Find the LCM of 180 and 182?

Answer:

Least Common Multiple of 180 and 182 = 16380

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 182

182 = 2 x 7 x 13

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

LCM = 16380 = 2 x 2 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 180 and 182 is 16380.