What is the Least Common Multiple of 30198 and 30205?

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 30205 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 30205, than apply into the LCM equation.

GCF(30198,30205) = 7
LCM(30198,30205) = ( 30198 × 30205) / 7
LCM(30198,30205) = 912130590 / 7
LCM(30198,30205) = 130304370

Least Common Multiple (LCM) of 30198 and 30205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30198 and 30205. First we will calculate the prime factors of 30198 and 30205.

Prime Factorization of 30198

Prime Factorization of 30205

Now multiplying the highest exponent prime factors to calculate the LCM of 30198 and 30205.

LCM(30198,30205) = 2¹ × 3¹ × 7¹ × 719¹ × 5¹ × 863¹
LCM(30198,30205) = 130304370