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What is the Least Common Multiple of 17472 and 17484?

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 17472 and 17484 is 25456704.

LCM(17472,17484) = 25456704

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Least Common Multiple of 17472 and 17484 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17472 and 17484, than apply into the LCM equation.

GCF(17472,17484) = 12
LCM(17472,17484) = ( 17472 × 17484) / 12
LCM(17472,17484) = 305480448 / 12
LCM(17472,17484) = 25456704

Least Common Multiple (LCM) of 17472 and 17484 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17472 and 17484. First we will calculate the prime factors of 17472 and 17484.

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

Prime Factorization of 17484

Prime factors of 17484 are 2, 3, 31, 47. Prime factorization of 17484 in exponential form is:

17484 = 22 × 31 × 311 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 17472 and 17484.

LCM(17472,17484) = 26 × 31 × 71 × 131 × 311 × 471
LCM(17472,17484) = 25456704