What is the Least Common Multiple of 30198 and 30208?

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 30198 and 30208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30198 and 30208, than apply into the LCM equation.

GCF(30198,30208) = 2
LCM(30198,30208) = ( 30198 × 30208) / 2
LCM(30198,30208) = 912221184 / 2
LCM(30198,30208) = 456110592

Least Common Multiple (LCM) of 30198 and 30208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30198 and 30208. First we will calculate the prime factors of 30198 and 30208.

Prime Factorization of 30198

Prime Factorization of 30208

Now multiplying the highest exponent prime factors to calculate the LCM of 30198 and 30208.

LCM(30198,30208) = 2⁹ × 3¹ × 7¹ × 719¹ × 59¹
LCM(30198,30208) = 456110592