What is the Least Common Multiple of 3565 and 3585?

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 3565 and 3585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3565 and 3585, than apply into the LCM equation.

GCF(3565,3585) = 5
LCM(3565,3585) = ( 3565 × 3585) / 5
LCM(3565,3585) = 12780525 / 5
LCM(3565,3585) = 2556105

Least Common Multiple (LCM) of 3565 and 3585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3565 and 3585. First we will calculate the prime factors of 3565 and 3585.

Prime Factorization of 3565

Prime Factorization of 3585

Now multiplying the highest exponent prime factors to calculate the LCM of 3565 and 3585.

LCM(3565,3585) = 5¹ × 23¹ × 31¹ × 3¹ × 239¹
LCM(3565,3585) = 2556105