What is the Least Common Multiple of 39105 and 39117?

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 39117 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 39117, than apply into the LCM equation.

GCF(39105,39117) = 3
LCM(39105,39117) = ( 39105 × 39117) / 3
LCM(39105,39117) = 1529670285 / 3
LCM(39105,39117) = 509890095

Least Common Multiple (LCM) of 39105 and 39117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39105 and 39117. First we will calculate the prime factors of 39105 and 39117.

Prime Factorization of 39105

Prime Factorization of 39117

Now multiplying the highest exponent prime factors to calculate the LCM of 39105 and 39117.

LCM(39105,39117) = 3² × 5¹ × 11¹ × 79¹ × 13¹ × 17¹ × 59¹
LCM(39105,39117) = 509890095