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What is the Least Common Multiple of 17634 and 17646?

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 17634 and 17646 is 51861594.

LCM(17634,17646) = 51861594

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Least Common Multiple of 17634 and 17646 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17634 and 17646, than apply into the LCM equation.

GCF(17634,17646) = 6
LCM(17634,17646) = ( 17634 × 17646) / 6
LCM(17634,17646) = 311169564 / 6
LCM(17634,17646) = 51861594

Least Common Multiple (LCM) of 17634 and 17646 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17634 and 17646. First we will calculate the prime factors of 17634 and 17646.

Prime Factorization of 17634

Prime factors of 17634 are 2, 3, 2939. Prime factorization of 17634 in exponential form is:

17634 = 21 × 31 × 29391

Prime Factorization of 17646

Prime factors of 17646 are 2, 3, 17, 173. Prime factorization of 17646 in exponential form is:

17646 = 21 × 31 × 171 × 1731

Now multiplying the highest exponent prime factors to calculate the LCM of 17634 and 17646.

LCM(17634,17646) = 21 × 31 × 29391 × 171 × 1731
LCM(17634,17646) = 51861594