What is the Least Common Multiple of 1565 and 1585?

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 1565 and 1585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1565 and 1585, than apply into the LCM equation.

GCF(1565,1585) = 5
LCM(1565,1585) = ( 1565 × 1585) / 5
LCM(1565,1585) = 2480525 / 5
LCM(1565,1585) = 496105

Least Common Multiple (LCM) of 1565 and 1585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1565 and 1585. First we will calculate the prime factors of 1565 and 1585.

Prime Factorization of 1565

Prime Factorization of 1585

Now multiplying the highest exponent prime factors to calculate the LCM of 1565 and 1585.

LCM(1565,1585) = 5¹ × 313¹ × 317¹
LCM(1565,1585) = 496105