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What is the Least Common Multiple of 17493 and 17506?

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 17493 and 17506 is 306232458.

LCM(17493,17506) = 306232458

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Least Common Multiple of 17493 and 17506 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17493 and 17506, than apply into the LCM equation.

GCF(17493,17506) = 1
LCM(17493,17506) = ( 17493 × 17506) / 1
LCM(17493,17506) = 306232458 / 1
LCM(17493,17506) = 306232458

Least Common Multiple (LCM) of 17493 and 17506 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17493 and 17506. First we will calculate the prime factors of 17493 and 17506.

Prime Factorization of 17493

Prime factors of 17493 are 3, 7, 17. Prime factorization of 17493 in exponential form is:

17493 = 31 × 73 × 171

Prime Factorization of 17506

Prime factors of 17506 are 2, 8753. Prime factorization of 17506 in exponential form is:

17506 = 21 × 87531

Now multiplying the highest exponent prime factors to calculate the LCM of 17493 and 17506.

LCM(17493,17506) = 31 × 73 × 171 × 21 × 87531
LCM(17493,17506) = 306232458