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What is the Least Common Multiple of 30070 and 30090?

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 30070 and 30090 is 90480630.

LCM(30070,30090) = 90480630

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Least Common Multiple of 30070 and 30090 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30070 and 30090, than apply into the LCM equation.

GCF(30070,30090) = 10
LCM(30070,30090) = ( 30070 × 30090) / 10
LCM(30070,30090) = 904806300 / 10
LCM(30070,30090) = 90480630

Least Common Multiple (LCM) of 30070 and 30090 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30070 and 30090. First we will calculate the prime factors of 30070 and 30090.

Prime Factorization of 30070

Prime factors of 30070 are 2, 5, 31, 97. Prime factorization of 30070 in exponential form is:

30070 = 21 × 51 × 311 × 971

Prime Factorization of 30090

Prime factors of 30090 are 2, 3, 5, 17, 59. Prime factorization of 30090 in exponential form is:

30090 = 21 × 31 × 51 × 171 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 30070 and 30090.

LCM(30070,30090) = 21 × 51 × 311 × 971 × 31 × 171 × 591
LCM(30070,30090) = 90480630