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What is the Least Common Multiple of 30100 and 30112?

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 30100 and 30112 is 226592800.

LCM(30100,30112) = 226592800

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Least Common Multiple of 30100 and 30112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30100 and 30112, than apply into the LCM equation.

GCF(30100,30112) = 4
LCM(30100,30112) = ( 30100 × 30112) / 4
LCM(30100,30112) = 906371200 / 4
LCM(30100,30112) = 226592800

Least Common Multiple (LCM) of 30100 and 30112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30100 and 30112. First we will calculate the prime factors of 30100 and 30112.

Prime Factorization of 30100

Prime factors of 30100 are 2, 5, 7, 43. Prime factorization of 30100 in exponential form is:

30100 = 22 × 52 × 71 × 431

Prime Factorization of 30112

Prime factors of 30112 are 2, 941. Prime factorization of 30112 in exponential form is:

30112 = 25 × 9411

Now multiplying the highest exponent prime factors to calculate the LCM of 30100 and 30112.

LCM(30100,30112) = 25 × 52 × 71 × 431 × 9411
LCM(30100,30112) = 226592800