What is the Least Common Multiple of 72105 and 72111?

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 72105 and 72111 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72105 and 72111, than apply into the LCM equation.

GCF(72105,72111) = 3
LCM(72105,72111) = ( 72105 × 72111) / 3
LCM(72105,72111) = 5199563655 / 3
LCM(72105,72111) = 1733187885

Least Common Multiple (LCM) of 72105 and 72111 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72105 and 72111. First we will calculate the prime factors of 72105 and 72111.

Prime Factorization of 72105

Prime Factorization of 72111

Now multiplying the highest exponent prime factors to calculate the LCM of 72105 and 72111.

LCM(72105,72111) = 3¹ × 5¹ × 11¹ × 19¹ × 23¹ × 13¹ × 43²
LCM(72105,72111) = 1733187885