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What is the Least Common Multiple of 30302 and 30312?

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 30302 and 30312 is 459257112.

LCM(30302,30312) = 459257112

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Least Common Multiple of 30302 and 30312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30302 and 30312, than apply into the LCM equation.

GCF(30302,30312) = 2
LCM(30302,30312) = ( 30302 × 30312) / 2
LCM(30302,30312) = 918514224 / 2
LCM(30302,30312) = 459257112

Least Common Multiple (LCM) of 30302 and 30312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30302 and 30312. First we will calculate the prime factors of 30302 and 30312.

Prime Factorization of 30302

Prime factors of 30302 are 2, 109, 139. Prime factorization of 30302 in exponential form is:

30302 = 21 × 1091 × 1391

Prime Factorization of 30312

Prime factors of 30312 are 2, 3, 421. Prime factorization of 30312 in exponential form is:

30312 = 23 × 32 × 4211

Now multiplying the highest exponent prime factors to calculate the LCM of 30302 and 30312.

LCM(30302,30312) = 23 × 1091 × 1391 × 32 × 4211
LCM(30302,30312) = 459257112