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What is the Least Common Multiple of 180 and 200?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 180 and 200 is 1800.

LCM(180,200) = 1800

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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

Least Common Multiple (LCM) of 180 and 200 with Primes

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

Prime factors of 180 are 2, 3, 5. Prime factorization of 180 in exponential form is:

180 = 22 × 32 × 51

Prime Factorization of 200

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