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What is the Least Common Multiple of 17993 and 18003?

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 17993 and 18003 is 323927979.

LCM(17993,18003) = 323927979

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Least Common Multiple of 17993 and 18003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17993 and 18003, than apply into the LCM equation.

GCF(17993,18003) = 1
LCM(17993,18003) = ( 17993 × 18003) / 1
LCM(17993,18003) = 323927979 / 1
LCM(17993,18003) = 323927979

Least Common Multiple (LCM) of 17993 and 18003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17993 and 18003. First we will calculate the prime factors of 17993 and 18003.

Prime Factorization of 17993

Prime factors of 17993 are 19, 947. Prime factorization of 17993 in exponential form is:

17993 = 191 × 9471

Prime Factorization of 18003

Prime factors of 18003 are 3, 17, 353. Prime factorization of 18003 in exponential form is:

18003 = 31 × 171 × 3531

Now multiplying the highest exponent prime factors to calculate the LCM of 17993 and 18003.

LCM(17993,18003) = 191 × 9471 × 31 × 171 × 3531
LCM(17993,18003) = 323927979