What is the Least Common Multiple of 30288 and 30300?

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 30288 and 30300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30288 and 30300, than apply into the LCM equation.

GCF(30288,30300) = 12
LCM(30288,30300) = ( 30288 × 30300) / 12
LCM(30288,30300) = 917726400 / 12
LCM(30288,30300) = 76477200

Least Common Multiple (LCM) of 30288 and 30300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30288 and 30300. First we will calculate the prime factors of 30288 and 30300.

Prime Factorization of 30288

Prime Factorization of 30300

Now multiplying the highest exponent prime factors to calculate the LCM of 30288 and 30300.

LCM(30288,30300) = 2⁴ × 3¹ × 631¹ × 5² × 101¹
LCM(30288,30300) = 76477200