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What is the Least Common Multiple of 10108 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 10108 and 10116 is 25563132.

LCM(10108,10116) = 25563132

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Least Common Multiple of 10108 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 10108 and 10116, than apply into the LCM equation.

GCF(10108,10116) = 4
LCM(10108,10116) = ( 10108 × 10116) / 4
LCM(10108,10116) = 102252528 / 4
LCM(10108,10116) = 25563132

Least Common Multiple (LCM) of 10108 and 10116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10108 and 10116. First we will calculate the prime factors of 10108 and 10116.

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 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 10108 and 10116.

LCM(10108,10116) = 22 × 71 × 192 × 32 × 2811
LCM(10108,10116) = 25563132