What is the Least Common Multiple of 37296 and 37305?

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 37296 and 37305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37296 and 37305, than apply into the LCM equation.

GCF(37296,37305) = 9
LCM(37296,37305) = ( 37296 × 37305) / 9
LCM(37296,37305) = 1391327280 / 9
LCM(37296,37305) = 154591920

Least Common Multiple (LCM) of 37296 and 37305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37296 and 37305. First we will calculate the prime factors of 37296 and 37305.

Prime Factorization of 37296

Prime Factorization of 37305

Now multiplying the highest exponent prime factors to calculate the LCM of 37296 and 37305.

LCM(37296,37305) = 2⁴ × 3² × 7¹ × 37¹ × 5¹ × 829¹
LCM(37296,37305) = 154591920