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What is the Least Common Multiple of 10101 and 10116?

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 10101 and 10116 is 34060572.

LCM(10101,10116) = 34060572

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Least Common Multiple of 10101 and 10116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10101 and 10116, than apply into the LCM equation.

GCF(10101,10116) = 3
LCM(10101,10116) = ( 10101 × 10116) / 3
LCM(10101,10116) = 102181716 / 3
LCM(10101,10116) = 34060572

Least Common Multiple (LCM) of 10101 and 10116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10101 and 10116. First we will calculate the prime factors of 10101 and 10116.

Prime Factorization of 10101

Prime factors of 10101 are 3, 7, 13, 37. Prime factorization of 10101 in exponential form is:

10101 = 31 × 71 × 131 × 371

Prime Factorization of 10116

Prime factors of 10116 are 2, 3, 281. Prime factorization of 10116 in exponential form is:

10116 = 22 × 32 × 2811

Now multiplying the highest exponent prime factors to calculate the LCM of 10101 and 10116.

LCM(10101,10116) = 32 × 71 × 131 × 371 × 22 × 2811
LCM(10101,10116) = 34060572