What is the Least Common Multiple of 30978 and 30992?

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 30978 and 30992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30978 and 30992, than apply into the LCM equation.

GCF(30978,30992) = 2
LCM(30978,30992) = ( 30978 × 30992) / 2
LCM(30978,30992) = 960070176 / 2
LCM(30978,30992) = 480035088

Least Common Multiple (LCM) of 30978 and 30992 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30978 and 30992. First we will calculate the prime factors of 30978 and 30992.

Prime Factorization of 30978

Prime Factorization of 30992

Now multiplying the highest exponent prime factors to calculate the LCM of 30978 and 30992.

LCM(30978,30992) = 2⁴ × 3² × 1721¹ × 13¹ × 149¹
LCM(30978,30992) = 480035088