What is the Least Common Multiple of 7296 and 7305?

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 7296 and 7305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7296 and 7305, than apply into the LCM equation.

GCF(7296,7305) = 3
LCM(7296,7305) = ( 7296 × 7305) / 3
LCM(7296,7305) = 53297280 / 3
LCM(7296,7305) = 17765760

Least Common Multiple (LCM) of 7296 and 7305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7296 and 7305. First we will calculate the prime factors of 7296 and 7305.

Prime Factorization of 7296

Prime Factorization of 7305

Now multiplying the highest exponent prime factors to calculate the LCM of 7296 and 7305.

LCM(7296,7305) = 2⁷ × 3¹ × 19¹ × 5¹ × 487¹
LCM(7296,7305) = 17765760