What is the Least Common Multiple of 30768 and 30780?

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 30768 and 30780 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30768 and 30780, than apply into the LCM equation.

GCF(30768,30780) = 12
LCM(30768,30780) = ( 30768 × 30780) / 12
LCM(30768,30780) = 947039040 / 12
LCM(30768,30780) = 78919920

Least Common Multiple (LCM) of 30768 and 30780 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30768 and 30780. First we will calculate the prime factors of 30768 and 30780.

Prime Factorization of 30768

Prime Factorization of 30780

Now multiplying the highest exponent prime factors to calculate the LCM of 30768 and 30780.

LCM(30768,30780) = 2⁴ × 3⁴ × 641¹ × 5¹ × 19¹
LCM(30768,30780) = 78919920