What is the Least Common Multiple of 39120 and 39140?

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 39120 and 39140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39120 and 39140, than apply into the LCM equation.

GCF(39120,39140) = 20
LCM(39120,39140) = ( 39120 × 39140) / 20
LCM(39120,39140) = 1531156800 / 20
LCM(39120,39140) = 76557840

Least Common Multiple (LCM) of 39120 and 39140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39120 and 39140. First we will calculate the prime factors of 39120 and 39140.

Prime Factorization of 39120

Prime Factorization of 39140

Now multiplying the highest exponent prime factors to calculate the LCM of 39120 and 39140.

LCM(39120,39140) = 2⁴ × 3¹ × 5¹ × 163¹ × 19¹ × 103¹
LCM(39120,39140) = 76557840