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What is the Least Common Multiple of 17700 and 17710?

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 17700 and 17710 is 31346700.

LCM(17700,17710) = 31346700

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Least Common Multiple of 17700 and 17710 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17700 and 17710, than apply into the LCM equation.

GCF(17700,17710) = 10
LCM(17700,17710) = ( 17700 × 17710) / 10
LCM(17700,17710) = 313467000 / 10
LCM(17700,17710) = 31346700

Least Common Multiple (LCM) of 17700 and 17710 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17700 and 17710. First we will calculate the prime factors of 17700 and 17710.

Prime Factorization of 17700

Prime factors of 17700 are 2, 3, 5, 59. Prime factorization of 17700 in exponential form is:

17700 = 22 × 31 × 52 × 591

Prime Factorization of 17710

Prime factors of 17710 are 2, 5, 7, 11, 23. Prime factorization of 17710 in exponential form is:

17710 = 21 × 51 × 71 × 111 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 17700 and 17710.

LCM(17700,17710) = 22 × 31 × 52 × 591 × 71 × 111 × 231
LCM(17700,17710) = 31346700