What is the Least Common Multiple of 39960 and 39965?

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 39960 and 39965 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39960 and 39965, than apply into the LCM equation.

GCF(39960,39965) = 5
LCM(39960,39965) = ( 39960 × 39965) / 5
LCM(39960,39965) = 1597001400 / 5
LCM(39960,39965) = 319400280

Least Common Multiple (LCM) of 39960 and 39965 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39960 and 39965. First we will calculate the prime factors of 39960 and 39965.

Prime Factorization of 39960

Prime Factorization of 39965

Now multiplying the highest exponent prime factors to calculate the LCM of 39960 and 39965.

LCM(39960,39965) = 2³ × 3³ × 5¹ × 37¹ × 7993¹
LCM(39960,39965) = 319400280