What is the Least Common Multiple of 30966 and 30975?

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 30966 and 30975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30966 and 30975, than apply into the LCM equation.

GCF(30966,30975) = 3
LCM(30966,30975) = ( 30966 × 30975) / 3
LCM(30966,30975) = 959171850 / 3
LCM(30966,30975) = 319723950

Least Common Multiple (LCM) of 30966 and 30975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30966 and 30975. First we will calculate the prime factors of 30966 and 30975.

Prime Factorization of 30966

Prime Factorization of 30975

Now multiplying the highest exponent prime factors to calculate the LCM of 30966 and 30975.

LCM(30966,30975) = 2¹ × 3¹ × 13¹ × 397¹ × 5² × 7¹ × 59¹
LCM(30966,30975) = 319723950