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What is the Least Common Multiple of 17661 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 17661 and 17678 is 312211158.

LCM(17661,17678) = 312211158

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Least Common Multiple of 17661 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 17661 and 17678, than apply into the LCM equation.

GCF(17661,17678) = 1
LCM(17661,17678) = ( 17661 × 17678) / 1
LCM(17661,17678) = 312211158 / 1
LCM(17661,17678) = 312211158

Least Common Multiple (LCM) of 17661 and 17678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17661 and 17678. First we will calculate the prime factors of 17661 and 17678.

Prime Factorization of 17661

Prime factors of 17661 are 3, 7, 29. Prime factorization of 17661 in exponential form is:

17661 = 31 × 71 × 292

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 17661 and 17678.

LCM(17661,17678) = 31 × 71 × 292 × 21 × 88391
LCM(17661,17678) = 312211158