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What is the Least Common Multiple of 30897 and 30912?

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 30897 and 30912 is 318362688.

LCM(30897,30912) = 318362688

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Least Common Multiple of 30897 and 30912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30897 and 30912, than apply into the LCM equation.

GCF(30897,30912) = 3
LCM(30897,30912) = ( 30897 × 30912) / 3
LCM(30897,30912) = 955088064 / 3
LCM(30897,30912) = 318362688

Least Common Multiple (LCM) of 30897 and 30912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30897 and 30912. First we will calculate the prime factors of 30897 and 30912.

Prime Factorization of 30897

Prime factors of 30897 are 3, 3433. Prime factorization of 30897 in exponential form is:

30897 = 32 × 34331

Prime Factorization of 30912

Prime factors of 30912 are 2, 3, 7, 23. Prime factorization of 30912 in exponential form is:

30912 = 26 × 31 × 71 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 30897 and 30912.

LCM(30897,30912) = 32 × 34331 × 26 × 71 × 231
LCM(30897,30912) = 318362688