What is the Least Common Multiple of 30208 and 30212?

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 30212 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 30212, than apply into the LCM equation.

GCF(30208,30212) = 4
LCM(30208,30212) = ( 30208 × 30212) / 4
LCM(30208,30212) = 912644096 / 4
LCM(30208,30212) = 228161024

Least Common Multiple (LCM) of 30208 and 30212 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30208 and 30212. First we will calculate the prime factors of 30208 and 30212.

Prime Factorization of 30208

Prime Factorization of 30212

Now multiplying the highest exponent prime factors to calculate the LCM of 30208 and 30212.

LCM(30208,30212) = 2⁹ × 59¹ × 7¹ × 13¹ × 83¹
LCM(30208,30212) = 228161024