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What is the Least Common Multiple of 30134 and 30142?

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 30134 and 30142 is 454149514.

LCM(30134,30142) = 454149514

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Least Common Multiple of 30134 and 30142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30134 and 30142, than apply into the LCM equation.

GCF(30134,30142) = 2
LCM(30134,30142) = ( 30134 × 30142) / 2
LCM(30134,30142) = 908299028 / 2
LCM(30134,30142) = 454149514

Least Common Multiple (LCM) of 30134 and 30142 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30134 and 30142. First we will calculate the prime factors of 30134 and 30142.

Prime Factorization of 30134

Prime factors of 30134 are 2, 13, 19, 61. Prime factorization of 30134 in exponential form is:

30134 = 21 × 131 × 191 × 611

Prime Factorization of 30142

Prime factors of 30142 are 2, 7, 2153. Prime factorization of 30142 in exponential form is:

30142 = 21 × 71 × 21531

Now multiplying the highest exponent prime factors to calculate the LCM of 30134 and 30142.

LCM(30134,30142) = 21 × 131 × 191 × 611 × 71 × 21531
LCM(30134,30142) = 454149514