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What is the Least Common Multiple of 10128 and 10142?

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 10128 and 10142 is 51359088.

LCM(10128,10142) = 51359088

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Least Common Multiple of 10128 and 10142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10128 and 10142, than apply into the LCM equation.

GCF(10128,10142) = 2
LCM(10128,10142) = ( 10128 × 10142) / 2
LCM(10128,10142) = 102718176 / 2
LCM(10128,10142) = 51359088

Least Common Multiple (LCM) of 10128 and 10142 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10128 and 10142. First we will calculate the prime factors of 10128 and 10142.

Prime Factorization of 10128

Prime factors of 10128 are 2, 3, 211. Prime factorization of 10128 in exponential form is:

10128 = 24 × 31 × 2111

Prime Factorization of 10142

Prime factors of 10142 are 2, 11, 461. Prime factorization of 10142 in exponential form is:

10142 = 21 × 111 × 4611

Now multiplying the highest exponent prime factors to calculate the LCM of 10128 and 10142.

LCM(10128,10142) = 24 × 31 × 2111 × 111 × 4611
LCM(10128,10142) = 51359088