What is the Least Common Multiple of 17580 and 17584?

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 of 17580 and 17584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17580 and 17584, than apply into the LCM equation.

GCF(17580,17584) = 4
LCM(17580,17584) = ( 17580 × 17584) / 4
LCM(17580,17584) = 309126720 / 4
LCM(17580,17584) = 77281680

Least Common Multiple (LCM) of 17580 and 17584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17580 and 17584. First we will calculate the prime factors of 17580 and 17584.

Prime Factorization of 17580

Prime Factorization of 17584

Now multiplying the highest exponent prime factors to calculate the LCM of 17580 and 17584.

LCM(17580,17584) = 2⁴ × 3¹ × 5¹ × 293¹ × 7¹ × 157¹
LCM(17580,17584) = 77281680