Least Common Multiple of 180 and 184

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 184 the smallest integer that is 8280 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 184 is 8280.

LCM(180,184) = 8280

LCM of 180 and 184

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

LCM of:
and

Least Common Multiple of 180 and 184

LCM of 180 and 184 is 8280

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 184. First we will calculate the prime factors of 180 and 184.

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 184


2 184
2 92
2 46
23 23
1

Prime factors of 184 are 2,23. Prime factorization of 184 in exponential form is:

184 = 23×231

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 184.

LCM(180,184) = 23×32×51×231
LCM(180,184) = 8280

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 184

List of positive integer factors of 184 that divides 184 without a remainder.

1, 2, 4, 8, 23, 46, 92, 184

Least Common Multiple of 180 and 184 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 184, than apply into the LCM equation.

GCF(180,184) = 4
LCM(180,184) = ( 180 × 184) / 4
LCM(180,184) = 33120 / 4
LCM(180,184) = 8280

Properties of LCM 180 and 184

(i) The LCM of 184 and 180 is associative

LCM of 180 and 184 = LCM of 184 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 184

Frequently Asked Questions on LCM of 180 and 184

1. What is the LCM of 180 and 184?

Answer: LCM of 180 and 184 is 8280.

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 184?

Answer: Factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184. There are 8 integers that are factors of 184. The greatest factor of 184 is 184.

4. How to Find the LCM of 180 and 184?

Answer:

Least Common Multiple of 180 and 184 = 8280

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 184

184 = 2 x 2 x 2 x 23

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

LCM = 8280 = 2 x 2 x 2 x 3 x 3 x 5 x 23

Step 4: Therefore, the least common multiple of 180 and 184 is 8280.