What is the Least Common Multiple of 30208 and 30216?

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 30208 and 30216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30208 and 30216, than apply into the LCM equation.

GCF(30208,30216) = 8
LCM(30208,30216) = ( 30208 × 30216) / 8
LCM(30208,30216) = 912764928 / 8
LCM(30208,30216) = 114095616

Least Common Multiple (LCM) of 30208 and 30216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30208 and 30216. First we will calculate the prime factors of 30208 and 30216.

Prime Factorization of 30208

Prime Factorization of 30216

Now multiplying the highest exponent prime factors to calculate the LCM of 30208 and 30216.

LCM(30208,30216) = 2⁹ × 59¹ × 3¹ × 1259¹
LCM(30208,30216) = 114095616