What is the Least Common Multiple of 10300 and 10305?

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 10300 and 10305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10300 and 10305, than apply into the LCM equation.

GCF(10300,10305) = 5
LCM(10300,10305) = ( 10300 × 10305) / 5
LCM(10300,10305) = 106141500 / 5
LCM(10300,10305) = 21228300

Least Common Multiple (LCM) of 10300 and 10305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10300 and 10305. First we will calculate the prime factors of 10300 and 10305.

Prime Factorization of 10300

Prime Factorization of 10305

Now multiplying the highest exponent prime factors to calculate the LCM of 10300 and 10305.

LCM(10300,10305) = 2² × 5² × 103¹ × 3² × 229¹
LCM(10300,10305) = 21228300