What is the Least Common Multiple of 10580 and 10585?

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 10580 and 10585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10580 and 10585, than apply into the LCM equation.

GCF(10580,10585) = 5
LCM(10580,10585) = ( 10580 × 10585) / 5
LCM(10580,10585) = 111989300 / 5
LCM(10580,10585) = 22397860

Least Common Multiple (LCM) of 10580 and 10585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10580 and 10585. First we will calculate the prime factors of 10580 and 10585.

Prime Factorization of 10580

Prime Factorization of 10585

Now multiplying the highest exponent prime factors to calculate the LCM of 10580 and 10585.

LCM(10580,10585) = 2² × 5¹ × 23² × 29¹ × 73¹
LCM(10580,10585) = 22397860