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What is the Least Common Multiple of 27998 and 28012?

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 27998 and 28012 is 392139988.

LCM(27998,28012) = 392139988

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Least Common Multiple of 27998 and 28012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27998 and 28012, than apply into the LCM equation.

GCF(27998,28012) = 2
LCM(27998,28012) = ( 27998 × 28012) / 2
LCM(27998,28012) = 784279976 / 2
LCM(27998,28012) = 392139988

Least Common Multiple (LCM) of 27998 and 28012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27998 and 28012. First we will calculate the prime factors of 27998 and 28012.

Prime Factorization of 27998

Prime factors of 27998 are 2, 13999. Prime factorization of 27998 in exponential form is:

27998 = 21 × 139991

Prime Factorization of 28012

Prime factors of 28012 are 2, 47, 149. Prime factorization of 28012 in exponential form is:

28012 = 22 × 471 × 1491

Now multiplying the highest exponent prime factors to calculate the LCM of 27998 and 28012.

LCM(27998,28012) = 22 × 139991 × 471 × 1491
LCM(27998,28012) = 392139988