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What is the Least Common Multiple of 12103 and 12116?

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 12103 and 12116 is 11279996.

LCM(12103,12116) = 11279996

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Least Common Multiple of 12103 and 12116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12103 and 12116, than apply into the LCM equation.

GCF(12103,12116) = 13
LCM(12103,12116) = ( 12103 × 12116) / 13
LCM(12103,12116) = 146639948 / 13
LCM(12103,12116) = 11279996

Least Common Multiple (LCM) of 12103 and 12116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12103 and 12116. First we will calculate the prime factors of 12103 and 12116.

Prime Factorization of 12103

Prime factors of 12103 are 7, 13, 19. Prime factorization of 12103 in exponential form is:

12103 = 72 × 131 × 191

Prime Factorization of 12116

Prime factors of 12116 are 2, 13, 233. Prime factorization of 12116 in exponential form is:

12116 = 22 × 131 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 12103 and 12116.

LCM(12103,12116) = 72 × 131 × 191 × 22 × 2331
LCM(12103,12116) = 11279996