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What is the Least Common Multiple of 10108 and 10115?

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 10108 and 10115 is 14606060.

LCM(10108,10115) = 14606060

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Least Common Multiple of 10108 and 10115 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10108 and 10115, than apply into the LCM equation.

GCF(10108,10115) = 7
LCM(10108,10115) = ( 10108 × 10115) / 7
LCM(10108,10115) = 102242420 / 7
LCM(10108,10115) = 14606060

Least Common Multiple (LCM) of 10108 and 10115 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10108 and 10115. First we will calculate the prime factors of 10108 and 10115.

Prime Factorization of 10108

Prime factors of 10108 are 2, 7, 19. Prime factorization of 10108 in exponential form is:

10108 = 22 × 71 × 192

Prime Factorization of 10115

Prime factors of 10115 are 5, 7, 17. Prime factorization of 10115 in exponential form is:

10115 = 51 × 71 × 172

Now multiplying the highest exponent prime factors to calculate the LCM of 10108 and 10115.

LCM(10108,10115) = 22 × 71 × 192 × 51 × 172
LCM(10108,10115) = 14606060