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What is the Least Common Multiple of 17109 and 17114?

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 17109 and 17114 is 292803426.

LCM(17109,17114) = 292803426

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Least Common Multiple of 17109 and 17114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17109 and 17114, than apply into the LCM equation.

GCF(17109,17114) = 1
LCM(17109,17114) = ( 17109 × 17114) / 1
LCM(17109,17114) = 292803426 / 1
LCM(17109,17114) = 292803426

Least Common Multiple (LCM) of 17109 and 17114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17109 and 17114. First we will calculate the prime factors of 17109 and 17114.

Prime Factorization of 17109

Prime factors of 17109 are 3, 1901. Prime factorization of 17109 in exponential form is:

17109 = 32 × 19011

Prime Factorization of 17114

Prime factors of 17114 are 2, 43, 199. Prime factorization of 17114 in exponential form is:

17114 = 21 × 431 × 1991

Now multiplying the highest exponent prime factors to calculate the LCM of 17109 and 17114.

LCM(17109,17114) = 32 × 19011 × 21 × 431 × 1991
LCM(17109,17114) = 292803426