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What is the Least Common Multiple of 17380 and 17384?

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 17380 and 17384 is 75533480.

LCM(17380,17384) = 75533480

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Least Common Multiple of 17380 and 17384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17380 and 17384, than apply into the LCM equation.

GCF(17380,17384) = 4
LCM(17380,17384) = ( 17380 × 17384) / 4
LCM(17380,17384) = 302133920 / 4
LCM(17380,17384) = 75533480

Least Common Multiple (LCM) of 17380 and 17384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17380 and 17384. First we will calculate the prime factors of 17380 and 17384.

Prime Factorization of 17380

Prime factors of 17380 are 2, 5, 11, 79. Prime factorization of 17380 in exponential form is:

17380 = 22 × 51 × 111 × 791

Prime Factorization of 17384

Prime factors of 17384 are 2, 41, 53. Prime factorization of 17384 in exponential form is:

17384 = 23 × 411 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 17380 and 17384.

LCM(17380,17384) = 23 × 51 × 111 × 791 × 411 × 531
LCM(17380,17384) = 75533480