What is the Least Common Multiple of 39105 and 39125?

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 39105 and 39125 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39105 and 39125, than apply into the LCM equation.

GCF(39105,39125) = 5
LCM(39105,39125) = ( 39105 × 39125) / 5
LCM(39105,39125) = 1529983125 / 5
LCM(39105,39125) = 305996625

Least Common Multiple (LCM) of 39105 and 39125 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39105 and 39125. First we will calculate the prime factors of 39105 and 39125.

Prime Factorization of 39105

Prime Factorization of 39125

Now multiplying the highest exponent prime factors to calculate the LCM of 39105 and 39125.

LCM(39105,39125) = 3² × 5³ × 11¹ × 79¹ × 313¹
LCM(39105,39125) = 305996625