What is the Least Common Multiple of 45999 and 46005?

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 45999 and 46005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45999 and 46005, than apply into the LCM equation.

GCF(45999,46005) = 3
LCM(45999,46005) = ( 45999 × 46005) / 3
LCM(45999,46005) = 2116183995 / 3
LCM(45999,46005) = 705394665

Least Common Multiple (LCM) of 45999 and 46005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45999 and 46005. First we will calculate the prime factors of 45999 and 46005.

Prime Factorization of 45999

Prime Factorization of 46005

Now multiplying the highest exponent prime factors to calculate the LCM of 45999 and 46005.

LCM(45999,46005) = 3² × 19¹ × 269¹ × 5¹ × 3067¹
LCM(45999,46005) = 705394665