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What is the Least Common Multiple of 27708 and 27714?

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 27708 and 27714 is 127983252.

LCM(27708,27714) = 127983252

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Least Common Multiple of 27708 and 27714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27708 and 27714, than apply into the LCM equation.

GCF(27708,27714) = 6
LCM(27708,27714) = ( 27708 × 27714) / 6
LCM(27708,27714) = 767899512 / 6
LCM(27708,27714) = 127983252

Least Common Multiple (LCM) of 27708 and 27714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27708 and 27714. First we will calculate the prime factors of 27708 and 27714.

Prime Factorization of 27708

Prime factors of 27708 are 2, 3, 2309. Prime factorization of 27708 in exponential form is:

27708 = 22 × 31 × 23091

Prime Factorization of 27714

Prime factors of 27714 are 2, 3, 31, 149. Prime factorization of 27714 in exponential form is:

27714 = 21 × 31 × 311 × 1491

Now multiplying the highest exponent prime factors to calculate the LCM of 27708 and 27714.

LCM(27708,27714) = 22 × 31 × 23091 × 311 × 1491
LCM(27708,27714) = 127983252