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What is the Least Common Multiple of 17742 and 17759?

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 17742 and 17759 is 315080178.

LCM(17742,17759) = 315080178

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Least Common Multiple of 17742 and 17759 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17742 and 17759, than apply into the LCM equation.

GCF(17742,17759) = 1
LCM(17742,17759) = ( 17742 × 17759) / 1
LCM(17742,17759) = 315080178 / 1
LCM(17742,17759) = 315080178

Least Common Multiple (LCM) of 17742 and 17759 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17742 and 17759. First we will calculate the prime factors of 17742 and 17759.

Prime Factorization of 17742

Prime factors of 17742 are 2, 3, 2957. Prime factorization of 17742 in exponential form is:

17742 = 21 × 31 × 29571

Prime Factorization of 17759

Prime factors of 17759 are 7, 43, 59. Prime factorization of 17759 in exponential form is:

17759 = 71 × 431 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 17742 and 17759.

LCM(17742,17759) = 21 × 31 × 29571 × 71 × 431 × 591
LCM(17742,17759) = 315080178