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What is the Least Common Multiple of 30063 and 30075?

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 30063 and 30075 is 301381575.

LCM(30063,30075) = 301381575

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Least Common Multiple of 30063 and 30075 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30063 and 30075, than apply into the LCM equation.

GCF(30063,30075) = 3
LCM(30063,30075) = ( 30063 × 30075) / 3
LCM(30063,30075) = 904144725 / 3
LCM(30063,30075) = 301381575

Least Common Multiple (LCM) of 30063 and 30075 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30063 and 30075. First we will calculate the prime factors of 30063 and 30075.

Prime Factorization of 30063

Prime factors of 30063 are 3, 11, 911. Prime factorization of 30063 in exponential form is:

30063 = 31 × 111 × 9111

Prime Factorization of 30075

Prime factors of 30075 are 3, 5, 401. Prime factorization of 30075 in exponential form is:

30075 = 31 × 52 × 4011

Now multiplying the highest exponent prime factors to calculate the LCM of 30063 and 30075.

LCM(30063,30075) = 31 × 111 × 9111 × 52 × 4011
LCM(30063,30075) = 301381575