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What is the Least Common Multiple of 30003 and 30015?

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 30003 and 30015 is 300180015.

LCM(30003,30015) = 300180015

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Least Common Multiple of 30003 and 30015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30003 and 30015, than apply into the LCM equation.

GCF(30003,30015) = 3
LCM(30003,30015) = ( 30003 × 30015) / 3
LCM(30003,30015) = 900540045 / 3
LCM(30003,30015) = 300180015

Least Common Multiple (LCM) of 30003 and 30015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30003 and 30015. First we will calculate the prime factors of 30003 and 30015.

Prime Factorization of 30003

Prime factors of 30003 are 3, 73, 137. Prime factorization of 30003 in exponential form is:

30003 = 31 × 731 × 1371

Prime Factorization of 30015

Prime factors of 30015 are 3, 5, 23, 29. Prime factorization of 30015 in exponential form is:

30015 = 32 × 51 × 231 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 30003 and 30015.

LCM(30003,30015) = 32 × 731 × 1371 × 51 × 231 × 291
LCM(30003,30015) = 300180015