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What is the Least Common Multiple of 30170 and 30180?

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 30170 and 30180 is 91053060.

LCM(30170,30180) = 91053060

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Least Common Multiple of 30170 and 30180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30170 and 30180, than apply into the LCM equation.

GCF(30170,30180) = 10
LCM(30170,30180) = ( 30170 × 30180) / 10
LCM(30170,30180) = 910530600 / 10
LCM(30170,30180) = 91053060

Least Common Multiple (LCM) of 30170 and 30180 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30170 and 30180. First we will calculate the prime factors of 30170 and 30180.

Prime Factorization of 30170

Prime factors of 30170 are 2, 5, 7, 431. Prime factorization of 30170 in exponential form is:

30170 = 21 × 51 × 71 × 4311

Prime Factorization of 30180

Prime factors of 30180 are 2, 3, 5, 503. Prime factorization of 30180 in exponential form is:

30180 = 22 × 31 × 51 × 5031

Now multiplying the highest exponent prime factors to calculate the LCM of 30170 and 30180.

LCM(30170,30180) = 22 × 51 × 71 × 4311 × 31 × 5031
LCM(30170,30180) = 91053060