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What is the Least Common Multiple of 17665 and 17678?

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 17665 and 17678 is 312281870.

LCM(17665,17678) = 312281870

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Least Common Multiple of 17665 and 17678 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17665 and 17678, than apply into the LCM equation.

GCF(17665,17678) = 1
LCM(17665,17678) = ( 17665 × 17678) / 1
LCM(17665,17678) = 312281870 / 1
LCM(17665,17678) = 312281870

Least Common Multiple (LCM) of 17665 and 17678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17665 and 17678. First we will calculate the prime factors of 17665 and 17678.

Prime Factorization of 17665

Prime factors of 17665 are 5, 3533. Prime factorization of 17665 in exponential form is:

17665 = 51 × 35331

Prime Factorization of 17678

Prime factors of 17678 are 2, 8839. Prime factorization of 17678 in exponential form is:

17678 = 21 × 88391

Now multiplying the highest exponent prime factors to calculate the LCM of 17665 and 17678.

LCM(17665,17678) = 51 × 35331 × 21 × 88391
LCM(17665,17678) = 312281870