What is the Least Common Multiple of 39105 and 39114?

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 39114 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 39114, than apply into the LCM equation.

GCF(39105,39114) = 9
LCM(39105,39114) = ( 39105 × 39114) / 9
LCM(39105,39114) = 1529552970 / 9
LCM(39105,39114) = 169950330

Least Common Multiple (LCM) of 39105 and 39114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39105 and 39114. First we will calculate the prime factors of 39105 and 39114.

Prime Factorization of 39105

Prime Factorization of 39114

Now multiplying the highest exponent prime factors to calculate the LCM of 39105 and 39114.

LCM(39105,39114) = 3² × 5¹ × 11¹ × 79¹ × 2¹ × 41¹ × 53¹
LCM(39105,39114) = 169950330