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What is the Least Common Multiple of 10137 and 10146?

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 10137 and 10146 is 34283334.

LCM(10137,10146) = 34283334

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Least Common Multiple of 10137 and 10146 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10137 and 10146, than apply into the LCM equation.

GCF(10137,10146) = 3
LCM(10137,10146) = ( 10137 × 10146) / 3
LCM(10137,10146) = 102850002 / 3
LCM(10137,10146) = 34283334

Least Common Multiple (LCM) of 10137 and 10146 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10137 and 10146. First we will calculate the prime factors of 10137 and 10146.

Prime Factorization of 10137

Prime factors of 10137 are 3, 31, 109. Prime factorization of 10137 in exponential form is:

10137 = 31 × 311 × 1091

Prime Factorization of 10146

Prime factors of 10146 are 2, 3, 19, 89. Prime factorization of 10146 in exponential form is:

10146 = 21 × 31 × 191 × 891

Now multiplying the highest exponent prime factors to calculate the LCM of 10137 and 10146.

LCM(10137,10146) = 31 × 311 × 1091 × 21 × 191 × 891
LCM(10137,10146) = 34283334