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What is the Least Common Multiple of 27465 and 27480?

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 27465 and 27480 is 50315880.

LCM(27465,27480) = 50315880

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Least Common Multiple of 27465 and 27480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27465 and 27480, than apply into the LCM equation.

GCF(27465,27480) = 15
LCM(27465,27480) = ( 27465 × 27480) / 15
LCM(27465,27480) = 754738200 / 15
LCM(27465,27480) = 50315880

Least Common Multiple (LCM) of 27465 and 27480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27465 and 27480. First we will calculate the prime factors of 27465 and 27480.

Prime Factorization of 27465

Prime factors of 27465 are 3, 5, 1831. Prime factorization of 27465 in exponential form is:

27465 = 31 × 51 × 18311

Prime Factorization of 27480

Prime factors of 27480 are 2, 3, 5, 229. Prime factorization of 27480 in exponential form is:

27480 = 23 × 31 × 51 × 2291

Now multiplying the highest exponent prime factors to calculate the LCM of 27465 and 27480.

LCM(27465,27480) = 31 × 51 × 18311 × 23 × 2291
LCM(27465,27480) = 50315880