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What is the Least Common Multiple of 2175 and 2180?

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 2175 and 2180 is 948300.

LCM(2175,2180) = 948300

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Least Common Multiple of 2175 and 2180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2175 and 2180, than apply into the LCM equation.

GCF(2175,2180) = 5
LCM(2175,2180) = ( 2175 × 2180) / 5
LCM(2175,2180) = 4741500 / 5
LCM(2175,2180) = 948300

Least Common Multiple (LCM) of 2175 and 2180 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2175 and 2180. First we will calculate the prime factors of 2175 and 2180.

Prime Factorization of 2175

Prime factors of 2175 are 3, 5, 29. Prime factorization of 2175 in exponential form is:

2175 = 31 × 52 × 291

Prime Factorization of 2180

Prime factors of 2180 are 2, 5, 109. Prime factorization of 2180 in exponential form is:

2180 = 22 × 51 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 2175 and 2180.

LCM(2175,2180) = 31 × 52 × 291 × 22 × 1091
LCM(2175,2180) = 948300