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What is the Least Common Multiple of 27978 and 27984?

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 27978 and 27984 is 130489392.

LCM(27978,27984) = 130489392

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Least Common Multiple of 27978 and 27984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27978 and 27984, than apply into the LCM equation.

GCF(27978,27984) = 6
LCM(27978,27984) = ( 27978 × 27984) / 6
LCM(27978,27984) = 782936352 / 6
LCM(27978,27984) = 130489392

Least Common Multiple (LCM) of 27978 and 27984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27978 and 27984. First we will calculate the prime factors of 27978 and 27984.

Prime Factorization of 27978

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

27978 = 21 × 31 × 46631

Prime Factorization of 27984

Prime factors of 27984 are 2, 3, 11, 53. Prime factorization of 27984 in exponential form is:

27984 = 24 × 31 × 111 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 27978 and 27984.

LCM(27978,27984) = 24 × 31 × 46631 × 111 × 531
LCM(27978,27984) = 130489392