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What is the Least Common Multiple of 17457 and 17472?

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 17457 and 17472 is 101669568.

LCM(17457,17472) = 101669568

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Least Common Multiple of 17457 and 17472 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17457 and 17472, than apply into the LCM equation.

GCF(17457,17472) = 3
LCM(17457,17472) = ( 17457 × 17472) / 3
LCM(17457,17472) = 305008704 / 3
LCM(17457,17472) = 101669568

Least Common Multiple (LCM) of 17457 and 17472 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17457 and 17472. First we will calculate the prime factors of 17457 and 17472.

Prime Factorization of 17457

Prime factors of 17457 are 3, 11, 23. Prime factorization of 17457 in exponential form is:

17457 = 31 × 111 × 232

Prime Factorization of 17472

Prime factors of 17472 are 2, 3, 7, 13. Prime factorization of 17472 in exponential form is:

17472 = 26 × 31 × 71 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 17457 and 17472.

LCM(17457,17472) = 31 × 111 × 232 × 26 × 71 × 131
LCM(17457,17472) = 101669568