What is the Least Common Multiple of 30005 and 30014?

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 30005 and 30014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30005 and 30014, than apply into the LCM equation.

GCF(30005,30014) = 1
LCM(30005,30014) = ( 30005 × 30014) / 1
LCM(30005,30014) = 900570070 / 1
LCM(30005,30014) = 900570070

Least Common Multiple (LCM) of 30005 and 30014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30005 and 30014. First we will calculate the prime factors of 30005 and 30014.

Prime Factorization of 30005

Prime Factorization of 30014

Now multiplying the highest exponent prime factors to calculate the LCM of 30005 and 30014.

LCM(30005,30014) = 5¹ × 17¹ × 353¹ × 2¹ × 43¹ × 349¹
LCM(30005,30014) = 900570070