What is the Least Common Multiple of 30100 and 30105?

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 30100 and 30105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30100 and 30105, than apply into the LCM equation.

GCF(30100,30105) = 5
LCM(30100,30105) = ( 30100 × 30105) / 5
LCM(30100,30105) = 906160500 / 5
LCM(30100,30105) = 181232100

Least Common Multiple (LCM) of 30100 and 30105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30100 and 30105. First we will calculate the prime factors of 30100 and 30105.

Prime Factorization of 30100

Prime Factorization of 30105

Now multiplying the highest exponent prime factors to calculate the LCM of 30100 and 30105.

LCM(30100,30105) = 2² × 5² × 7¹ × 43¹ × 3³ × 223¹
LCM(30100,30105) = 181232100