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What is the Least Common Multiple of 30645 and 30663?

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 30645 and 30663 is 104407515.

LCM(30645,30663) = 104407515

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Least Common Multiple of 30645 and 30663 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30645 and 30663, than apply into the LCM equation.

GCF(30645,30663) = 9
LCM(30645,30663) = ( 30645 × 30663) / 9
LCM(30645,30663) = 939667635 / 9
LCM(30645,30663) = 104407515

Least Common Multiple (LCM) of 30645 and 30663 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30645 and 30663. First we will calculate the prime factors of 30645 and 30663.

Prime Factorization of 30645

Prime factors of 30645 are 3, 5, 227. Prime factorization of 30645 in exponential form is:

30645 = 33 × 51 × 2271

Prime Factorization of 30663

Prime factors of 30663 are 3, 3407. Prime factorization of 30663 in exponential form is:

30663 = 32 × 34071

Now multiplying the highest exponent prime factors to calculate the LCM of 30645 and 30663.

LCM(30645,30663) = 33 × 51 × 2271 × 34071
LCM(30645,30663) = 104407515