What is the Least Common Multiple of 29973 and 29985?

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 29973 and 29985 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29973 and 29985, than apply into the LCM equation.

GCF(29973,29985) = 3
LCM(29973,29985) = ( 29973 × 29985) / 3
LCM(29973,29985) = 898740405 / 3
LCM(29973,29985) = 299580135

Least Common Multiple (LCM) of 29973 and 29985 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29973 and 29985. First we will calculate the prime factors of 29973 and 29985.

Prime Factorization of 29973

Prime Factorization of 29985

Now multiplying the highest exponent prime factors to calculate the LCM of 29973 and 29985.

LCM(29973,29985) = 3¹ × 97¹ × 103¹ × 5¹ × 1999¹
LCM(29973,29985) = 299580135