What is the Least Common Multiple of 30305 and 30320?

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 30305 and 30320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30305 and 30320, than apply into the LCM equation.

GCF(30305,30320) = 5
LCM(30305,30320) = ( 30305 × 30320) / 5
LCM(30305,30320) = 918847600 / 5
LCM(30305,30320) = 183769520

Least Common Multiple (LCM) of 30305 and 30320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30305 and 30320. First we will calculate the prime factors of 30305 and 30320.

Prime Factorization of 30305

Prime Factorization of 30320

Now multiplying the highest exponent prime factors to calculate the LCM of 30305 and 30320.

LCM(30305,30320) = 5¹ × 11¹ × 19¹ × 29¹ × 2⁴ × 379¹
LCM(30305,30320) = 183769520