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What is the Least Common Multiple of 30489 and 30504?

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 30489 and 30504 is 310012152.

LCM(30489,30504) = 310012152

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Least Common Multiple of 30489 and 30504 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30489 and 30504, than apply into the LCM equation.

GCF(30489,30504) = 3
LCM(30489,30504) = ( 30489 × 30504) / 3
LCM(30489,30504) = 930036456 / 3
LCM(30489,30504) = 310012152

Least Common Multiple (LCM) of 30489 and 30504 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30489 and 30504. First we will calculate the prime factors of 30489 and 30504.

Prime Factorization of 30489

Prime factors of 30489 are 3, 10163. Prime factorization of 30489 in exponential form is:

30489 = 31 × 101631

Prime Factorization of 30504

Prime factors of 30504 are 2, 3, 31, 41. Prime factorization of 30504 in exponential form is:

30504 = 23 × 31 × 311 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 30489 and 30504.

LCM(30489,30504) = 31 × 101631 × 23 × 311 × 411
LCM(30489,30504) = 310012152