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What is the Least Common Multiple of 17997 and 18009?

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 17997 and 18009 is 108035991.

LCM(17997,18009) = 108035991

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Least Common Multiple of 17997 and 18009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17997 and 18009, than apply into the LCM equation.

GCF(17997,18009) = 3
LCM(17997,18009) = ( 17997 × 18009) / 3
LCM(17997,18009) = 324107973 / 3
LCM(17997,18009) = 108035991

Least Common Multiple (LCM) of 17997 and 18009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17997 and 18009. First we will calculate the prime factors of 17997 and 18009.

Prime Factorization of 17997

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

17997 = 31 × 71 × 8571

Prime Factorization of 18009

Prime factors of 18009 are 3, 23, 29. Prime factorization of 18009 in exponential form is:

18009 = 33 × 231 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 17997 and 18009.

LCM(17997,18009) = 33 × 71 × 8571 × 231 × 291
LCM(17997,18009) = 108035991