What is the Least Common Multiple of 72705 and 72720?

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 72705 and 72720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72705 and 72720, than apply into the LCM equation.

GCF(72705,72720) = 15
LCM(72705,72720) = ( 72705 × 72720) / 15
LCM(72705,72720) = 5287107600 / 15
LCM(72705,72720) = 352473840

Least Common Multiple (LCM) of 72705 and 72720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72705 and 72720. First we will calculate the prime factors of 72705 and 72720.

Prime Factorization of 72705

Prime Factorization of 72720

Now multiplying the highest exponent prime factors to calculate the LCM of 72705 and 72720.

LCM(72705,72720) = 3² × 5¹ × 37¹ × 131¹ × 2⁴ × 101¹
LCM(72705,72720) = 352473840