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What is the Least Common Multiple of 17733 and 17752?

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 17733 and 17752 is 314796216.

LCM(17733,17752) = 314796216

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Least Common Multiple of 17733 and 17752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17733 and 17752, than apply into the LCM equation.

GCF(17733,17752) = 1
LCM(17733,17752) = ( 17733 × 17752) / 1
LCM(17733,17752) = 314796216 / 1
LCM(17733,17752) = 314796216

Least Common Multiple (LCM) of 17733 and 17752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17733 and 17752. First we will calculate the prime factors of 17733 and 17752.

Prime Factorization of 17733

Prime factors of 17733 are 3, 23, 257. Prime factorization of 17733 in exponential form is:

17733 = 31 × 231 × 2571

Prime Factorization of 17752

Prime factors of 17752 are 2, 7, 317. Prime factorization of 17752 in exponential form is:

17752 = 23 × 71 × 3171

Now multiplying the highest exponent prime factors to calculate the LCM of 17733 and 17752.

LCM(17733,17752) = 31 × 231 × 2571 × 23 × 71 × 3171
LCM(17733,17752) = 314796216