What is the Least Common Multiple of 39960 and 39975?

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 39960 and 39975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39960 and 39975, than apply into the LCM equation.

GCF(39960,39975) = 15
LCM(39960,39975) = ( 39960 × 39975) / 15
LCM(39960,39975) = 1597401000 / 15
LCM(39960,39975) = 106493400

Least Common Multiple (LCM) of 39960 and 39975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39960 and 39975. First we will calculate the prime factors of 39960 and 39975.

Prime Factorization of 39960

Prime Factorization of 39975

Now multiplying the highest exponent prime factors to calculate the LCM of 39960 and 39975.

LCM(39960,39975) = 2³ × 3³ × 5² × 37¹ × 13¹ × 41¹
LCM(39960,39975) = 106493400