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What is the Least Common Multiple of 10100 and 10108?

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 10100 and 10108 is 25522700.

LCM(10100,10108) = 25522700

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Least Common Multiple of 10100 and 10108 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10100 and 10108, than apply into the LCM equation.

GCF(10100,10108) = 4
LCM(10100,10108) = ( 10100 × 10108) / 4
LCM(10100,10108) = 102090800 / 4
LCM(10100,10108) = 25522700

Least Common Multiple (LCM) of 10100 and 10108 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10100 and 10108. First we will calculate the prime factors of 10100 and 10108.

Prime Factorization of 10100

Prime factors of 10100 are 2, 5, 101. Prime factorization of 10100 in exponential form is:

10100 = 22 × 52 × 1011

Prime Factorization of 10108

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

10108 = 22 × 71 × 192

Now multiplying the highest exponent prime factors to calculate the LCM of 10100 and 10108.

LCM(10100,10108) = 22 × 52 × 1011 × 71 × 192
LCM(10100,10108) = 25522700