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What is the Least Common Multiple of 27714 and 27728?

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 27714 and 27728 is 384226896.

LCM(27714,27728) = 384226896

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Least Common Multiple of 27714 and 27728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27714 and 27728, than apply into the LCM equation.

GCF(27714,27728) = 2
LCM(27714,27728) = ( 27714 × 27728) / 2
LCM(27714,27728) = 768453792 / 2
LCM(27714,27728) = 384226896

Least Common Multiple (LCM) of 27714 and 27728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27714 and 27728. First we will calculate the prime factors of 27714 and 27728.

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

Prime Factorization of 27728

Prime factors of 27728 are 2, 1733. Prime factorization of 27728 in exponential form is:

27728 = 24 × 17331

Now multiplying the highest exponent prime factors to calculate the LCM of 27714 and 27728.

LCM(27714,27728) = 24 × 31 × 311 × 1491 × 17331
LCM(27714,27728) = 384226896