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What is the Least Common Multiple of 30372 and 30384?

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 30372 and 30384 is 76901904.

LCM(30372,30384) = 76901904

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Least Common Multiple of 30372 and 30384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30372 and 30384, than apply into the LCM equation.

GCF(30372,30384) = 12
LCM(30372,30384) = ( 30372 × 30384) / 12
LCM(30372,30384) = 922822848 / 12
LCM(30372,30384) = 76901904

Least Common Multiple (LCM) of 30372 and 30384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30372 and 30384. First we will calculate the prime factors of 30372 and 30384.

Prime Factorization of 30372

Prime factors of 30372 are 2, 3, 2531. Prime factorization of 30372 in exponential form is:

30372 = 22 × 31 × 25311

Prime Factorization of 30384

Prime factors of 30384 are 2, 3, 211. Prime factorization of 30384 in exponential form is:

30384 = 24 × 32 × 2111

Now multiplying the highest exponent prime factors to calculate the LCM of 30372 and 30384.

LCM(30372,30384) = 24 × 32 × 25311 × 2111
LCM(30372,30384) = 76901904