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What is the Least Common Multiple of 30032 and 30038?

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 30032 and 30038 is 451050608.

LCM(30032,30038) = 451050608

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Least Common Multiple of 30032 and 30038 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30032 and 30038, than apply into the LCM equation.

GCF(30032,30038) = 2
LCM(30032,30038) = ( 30032 × 30038) / 2
LCM(30032,30038) = 902101216 / 2
LCM(30032,30038) = 451050608

Least Common Multiple (LCM) of 30032 and 30038 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30032 and 30038. First we will calculate the prime factors of 30032 and 30038.

Prime Factorization of 30032

Prime factors of 30032 are 2, 1877. Prime factorization of 30032 in exponential form is:

30032 = 24 × 18771

Prime Factorization of 30038

Prime factors of 30038 are 2, 23, 653. Prime factorization of 30038 in exponential form is:

30038 = 21 × 231 × 6531

Now multiplying the highest exponent prime factors to calculate the LCM of 30032 and 30038.

LCM(30032,30038) = 24 × 18771 × 231 × 6531
LCM(30032,30038) = 451050608