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What is the Least Common Multiple of 27675 and 27680?

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 27675 and 27680 is 153208800.

LCM(27675,27680) = 153208800

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Least Common Multiple of 27675 and 27680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27675 and 27680, than apply into the LCM equation.

GCF(27675,27680) = 5
LCM(27675,27680) = ( 27675 × 27680) / 5
LCM(27675,27680) = 766044000 / 5
LCM(27675,27680) = 153208800

Least Common Multiple (LCM) of 27675 and 27680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27675 and 27680. First we will calculate the prime factors of 27675 and 27680.

Prime Factorization of 27675

Prime factors of 27675 are 3, 5, 41. Prime factorization of 27675 in exponential form is:

27675 = 33 × 52 × 411

Prime Factorization of 27680

Prime factors of 27680 are 2, 5, 173. Prime factorization of 27680 in exponential form is:

27680 = 25 × 51 × 1731

Now multiplying the highest exponent prime factors to calculate the LCM of 27675 and 27680.

LCM(27675,27680) = 33 × 52 × 411 × 25 × 1731
LCM(27675,27680) = 153208800