What is the Least Common Multiple of 39578 and 39585?

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 39578 and 39585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39578 and 39585, than apply into the LCM equation.

GCF(39578,39585) = 7
LCM(39578,39585) = ( 39578 × 39585) / 7
LCM(39578,39585) = 1566695130 / 7
LCM(39578,39585) = 223813590

Least Common Multiple (LCM) of 39578 and 39585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39578 and 39585. First we will calculate the prime factors of 39578 and 39585.

Prime Factorization of 39578

Prime Factorization of 39585

Now multiplying the highest exponent prime factors to calculate the LCM of 39578 and 39585.

LCM(39578,39585) = 2¹ × 7¹ × 11¹ × 257¹ × 3¹ × 5¹ × 13¹ × 29¹
LCM(39578,39585) = 223813590