What is the Least Common Multiple of 30780 and 30800?

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 30780 and 30800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30780 and 30800, than apply into the LCM equation.

GCF(30780,30800) = 20
LCM(30780,30800) = ( 30780 × 30800) / 20
LCM(30780,30800) = 948024000 / 20
LCM(30780,30800) = 47401200

Least Common Multiple (LCM) of 30780 and 30800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30780 and 30800. First we will calculate the prime factors of 30780 and 30800.

Prime Factorization of 30780

Prime Factorization of 30800

Now multiplying the highest exponent prime factors to calculate the LCM of 30780 and 30800.

LCM(30780,30800) = 2⁴ × 3⁴ × 5² × 19¹ × 7¹ × 11¹
LCM(30780,30800) = 47401200