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What is the Least Common Multiple of 10128 and 10140?

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 10140 is 8558160.

LCM(10128,10140) = 8558160

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Least Common Multiple of 10128 and 10140 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 10140, than apply into the LCM equation.

GCF(10128,10140) = 12
LCM(10128,10140) = ( 10128 × 10140) / 12
LCM(10128,10140) = 102697920 / 12
LCM(10128,10140) = 8558160

Least Common Multiple (LCM) of 10128 and 10140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10128 and 10140. First we will calculate the prime factors of 10128 and 10140.

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 10140

Prime factors of 10140 are 2, 3, 5, 13. Prime factorization of 10140 in exponential form is:

10140 = 22 × 31 × 51 × 132

Now multiplying the highest exponent prime factors to calculate the LCM of 10128 and 10140.

LCM(10128,10140) = 24 × 31 × 2111 × 51 × 132
LCM(10128,10140) = 8558160