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What is the Least Common Multiple of 17985 and 17997?

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 17985 and 17997 is 107892015.

LCM(17985,17997) = 107892015

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Least Common Multiple of 17985 and 17997 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17985 and 17997, than apply into the LCM equation.

GCF(17985,17997) = 3
LCM(17985,17997) = ( 17985 × 17997) / 3
LCM(17985,17997) = 323676045 / 3
LCM(17985,17997) = 107892015

Least Common Multiple (LCM) of 17985 and 17997 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17985 and 17997. First we will calculate the prime factors of 17985 and 17997.

Prime Factorization of 17985

Prime factors of 17985 are 3, 5, 11, 109. Prime factorization of 17985 in exponential form is:

17985 = 31 × 51 × 111 × 1091

Prime Factorization of 17997

Prime factors of 17997 are 3, 7, 857. Prime factorization of 17997 in exponential form is:

17997 = 31 × 71 × 8571

Now multiplying the highest exponent prime factors to calculate the LCM of 17985 and 17997.

LCM(17985,17997) = 31 × 51 × 111 × 1091 × 71 × 8571
LCM(17985,17997) = 107892015