What is the Least Common Multiple of 39945 and 39960?

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 39945 and 39960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39945 and 39960, than apply into the LCM equation.

GCF(39945,39960) = 15
LCM(39945,39960) = ( 39945 × 39960) / 15
LCM(39945,39960) = 1596202200 / 15
LCM(39945,39960) = 106413480

Least Common Multiple (LCM) of 39945 and 39960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39945 and 39960. First we will calculate the prime factors of 39945 and 39960.

Prime Factorization of 39945

Prime Factorization of 39960

Now multiplying the highest exponent prime factors to calculate the LCM of 39945 and 39960.

LCM(39945,39960) = 3³ × 5¹ × 2663¹ × 2³ × 37¹
LCM(39945,39960) = 106413480