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What is the Least Common Multiple of 30034 and 30042?

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 30034 and 30042 is 451140714.

LCM(30034,30042) = 451140714

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Least Common Multiple of 30034 and 30042 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30034 and 30042, than apply into the LCM equation.

GCF(30034,30042) = 2
LCM(30034,30042) = ( 30034 × 30042) / 2
LCM(30034,30042) = 902281428 / 2
LCM(30034,30042) = 451140714

Least Common Multiple (LCM) of 30034 and 30042 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30034 and 30042. First we will calculate the prime factors of 30034 and 30042.

Prime Factorization of 30034

Prime factors of 30034 are 2, 15017. Prime factorization of 30034 in exponential form is:

30034 = 21 × 150171

Prime Factorization of 30042

Prime factors of 30042 are 2, 3, 1669. Prime factorization of 30042 in exponential form is:

30042 = 21 × 32 × 16691

Now multiplying the highest exponent prime factors to calculate the LCM of 30034 and 30042.

LCM(30034,30042) = 21 × 150171 × 32 × 16691
LCM(30034,30042) = 451140714