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What is the Least Common Multiple of 67664 and 67678?

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 67664 and 67678 is 2289682096.

LCM(67664,67678) = 2289682096

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Least Common Multiple of 67664 and 67678 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67664 and 67678, than apply into the LCM equation.

GCF(67664,67678) = 2
LCM(67664,67678) = ( 67664 × 67678) / 2
LCM(67664,67678) = 4579364192 / 2
LCM(67664,67678) = 2289682096

Least Common Multiple (LCM) of 67664 and 67678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67664 and 67678. First we will calculate the prime factors of 67664 and 67678.

Prime Factorization of 67664

Prime factors of 67664 are 2, 4229. Prime factorization of 67664 in exponential form is:

67664 = 24 × 42291

Prime Factorization of 67678

Prime factors of 67678 are 2, 13, 19, 137. Prime factorization of 67678 in exponential form is:

67678 = 21 × 131 × 191 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 67664 and 67678.

LCM(67664,67678) = 24 × 42291 × 131 × 191 × 1371
LCM(67664,67678) = 2289682096