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What is the Least Common Multiple of 30465 and 30480?

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 30465 and 30480 is 61904880.

LCM(30465,30480) = 61904880

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Least Common Multiple of 30465 and 30480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30465 and 30480, than apply into the LCM equation.

GCF(30465,30480) = 15
LCM(30465,30480) = ( 30465 × 30480) / 15
LCM(30465,30480) = 928573200 / 15
LCM(30465,30480) = 61904880

Least Common Multiple (LCM) of 30465 and 30480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30465 and 30480. First we will calculate the prime factors of 30465 and 30480.

Prime Factorization of 30465

Prime factors of 30465 are 3, 5, 677. Prime factorization of 30465 in exponential form is:

30465 = 32 × 51 × 6771

Prime Factorization of 30480

Prime factors of 30480 are 2, 3, 5, 127. Prime factorization of 30480 in exponential form is:

30480 = 24 × 31 × 51 × 1271

Now multiplying the highest exponent prime factors to calculate the LCM of 30465 and 30480.

LCM(30465,30480) = 32 × 51 × 6771 × 24 × 1271
LCM(30465,30480) = 61904880