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What is the Least Common Multiple of 27404 and 27417?

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 27404 and 27417 is 57795036.

LCM(27404,27417) = 57795036

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Least Common Multiple of 27404 and 27417 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27404 and 27417, than apply into the LCM equation.

GCF(27404,27417) = 13
LCM(27404,27417) = ( 27404 × 27417) / 13
LCM(27404,27417) = 751335468 / 13
LCM(27404,27417) = 57795036

Least Common Multiple (LCM) of 27404 and 27417 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27404 and 27417. First we will calculate the prime factors of 27404 and 27417.

Prime Factorization of 27404

Prime factors of 27404 are 2, 13, 17, 31. Prime factorization of 27404 in exponential form is:

27404 = 22 × 131 × 171 × 311

Prime Factorization of 27417

Prime factors of 27417 are 3, 13, 19, 37. Prime factorization of 27417 in exponential form is:

27417 = 31 × 131 × 191 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 27404 and 27417.

LCM(27404,27417) = 22 × 131 × 171 × 311 × 31 × 191 × 371
LCM(27404,27417) = 57795036