What is the Least Common Multiple of 30009 and 30013?

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 30009 and 30013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30009 and 30013, than apply into the LCM equation.

GCF(30009,30013) = 1
LCM(30009,30013) = ( 30009 × 30013) / 1
LCM(30009,30013) = 900660117 / 1
LCM(30009,30013) = 900660117

Least Common Multiple (LCM) of 30009 and 30013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30009 and 30013. First we will calculate the prime factors of 30009 and 30013.

Prime Factorization of 30009

Prime Factorization of 30013

Now multiplying the highest exponent prime factors to calculate the LCM of 30009 and 30013.

LCM(30009,30013) = 3¹ × 7¹ × 1429¹ × 30013¹
LCM(30009,30013) = 900660117