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What is the Least Common Multiple of 27962 and 27978?

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 27962 and 27978 is 391160418.

LCM(27962,27978) = 391160418

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Least Common Multiple of 27962 and 27978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27962 and 27978, than apply into the LCM equation.

GCF(27962,27978) = 2
LCM(27962,27978) = ( 27962 × 27978) / 2
LCM(27962,27978) = 782320836 / 2
LCM(27962,27978) = 391160418

Least Common Multiple (LCM) of 27962 and 27978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27962 and 27978. First we will calculate the prime factors of 27962 and 27978.

Prime Factorization of 27962

Prime factors of 27962 are 2, 11, 31, 41. Prime factorization of 27962 in exponential form is:

27962 = 21 × 111 × 311 × 411

Prime Factorization of 27978

Prime factors of 27978 are 2, 3, 4663. Prime factorization of 27978 in exponential form is:

27978 = 21 × 31 × 46631

Now multiplying the highest exponent prime factors to calculate the LCM of 27962 and 27978.

LCM(27962,27978) = 21 × 111 × 311 × 411 × 31 × 46631
LCM(27962,27978) = 391160418