What is the Least Common Multiple of 69960 and 69975?

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 69960 and 69975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69960 and 69975, than apply into the LCM equation.

GCF(69960,69975) = 15
LCM(69960,69975) = ( 69960 × 69975) / 15
LCM(69960,69975) = 4895451000 / 15
LCM(69960,69975) = 326363400

Least Common Multiple (LCM) of 69960 and 69975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69960 and 69975. First we will calculate the prime factors of 69960 and 69975.

Prime Factorization of 69960

Prime Factorization of 69975

Now multiplying the highest exponent prime factors to calculate the LCM of 69960 and 69975.

LCM(69960,69975) = 2³ × 3² × 5² × 11¹ × 53¹ × 311¹
LCM(69960,69975) = 326363400