What is the Least Common Multiple of 9945 and 9960?

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 9945 and 9960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9945 and 9960, than apply into the LCM equation.

GCF(9945,9960) = 15
LCM(9945,9960) = ( 9945 × 9960) / 15
LCM(9945,9960) = 99052200 / 15
LCM(9945,9960) = 6603480

Least Common Multiple (LCM) of 9945 and 9960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9945 and 9960. First we will calculate the prime factors of 9945 and 9960.

Prime Factorization of 9945

Prime Factorization of 9960

Now multiplying the highest exponent prime factors to calculate the LCM of 9945 and 9960.

LCM(9945,9960) = 3² × 5¹ × 13¹ × 17¹ × 2³ × 83¹
LCM(9945,9960) = 6603480