Least Common Multiple of 180 and 200

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 200 the smallest integer that is 1800 that is divisible by both numbers.

Least Common Multiple (LCM) of 180 and 200 is 1800.

LCM(180,200) = 1800

LCM of 180 and 200

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

LCM of:
and

Least Common Multiple of 180 and 200

LCM of 180 and 200 is 1800

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 200. First we will calculate the prime factors of 180 and 200.

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 200


2 200
2 100
2 50
5 25
5 5
1

Prime factors of 200 are 2,5. Prime factorization of 200 in exponential form is:

200 = 23×52

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 200.

LCM(180,200) = 23×32×52
LCM(180,200) = 1800

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 200

List of positive integer factors of 200 that divides 200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Least Common Multiple of 180 and 200 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 200, than apply into the LCM equation.

GCF(180,200) = 20
LCM(180,200) = ( 180 × 200) / 20
LCM(180,200) = 36000 / 20
LCM(180,200) = 1800

Properties of LCM 180 and 200

(i) The LCM of 200 and 180 is associative

LCM of 180 and 200 = LCM of 200 and 180

Related Least Common Multiples of 180

Related Least Common Multiples of 200

Frequently Asked Questions on LCM of 180 and 200

1. What is the LCM of 180 and 200?

Answer: LCM of 180 and 200 is 1800.

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 200?

Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.

4. How to Find the LCM of 180 and 200?

Answer:

Least Common Multiple of 180 and 200 = 1800

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 200

200 = 2 x 2 x 2 x 5 x 5

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

LCM = 1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 180 and 200 is 1800.