What is the Least Common Multiple of 36945 and 36960?

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 36945 and 36960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36945 and 36960, than apply into the LCM equation.

GCF(36945,36960) = 15
LCM(36945,36960) = ( 36945 × 36960) / 15
LCM(36945,36960) = 1365487200 / 15
LCM(36945,36960) = 91032480

Least Common Multiple (LCM) of 36945 and 36960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36945 and 36960. First we will calculate the prime factors of 36945 and 36960.

Prime Factorization of 36945

Prime Factorization of 36960

Now multiplying the highest exponent prime factors to calculate the LCM of 36945 and 36960.

LCM(36945,36960) = 3² × 5¹ × 821¹ × 2⁵ × 7¹ × 11¹
LCM(36945,36960) = 91032480