What is the Least Common Multiple of 39975 and 39988?

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 39975 and 39988 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39975 and 39988, than apply into the LCM equation.

GCF(39975,39988) = 13
LCM(39975,39988) = ( 39975 × 39988) / 13
LCM(39975,39988) = 1598520300 / 13
LCM(39975,39988) = 122963100

Least Common Multiple (LCM) of 39975 and 39988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39975 and 39988. First we will calculate the prime factors of 39975 and 39988.

Prime Factorization of 39975

Prime Factorization of 39988

Now multiplying the highest exponent prime factors to calculate the LCM of 39975 and 39988.

LCM(39975,39988) = 3¹ × 5² × 13¹ × 41¹ × 2² × 769¹
LCM(39975,39988) = 122963100