What is the Least Common Multiple of 30030 and 30040?

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 30030 and 30040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30030 and 30040, than apply into the LCM equation.

GCF(30030,30040) = 10
LCM(30030,30040) = ( 30030 × 30040) / 10
LCM(30030,30040) = 902101200 / 10
LCM(30030,30040) = 90210120

Least Common Multiple (LCM) of 30030 and 30040 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30030 and 30040. First we will calculate the prime factors of 30030 and 30040.

Prime Factorization of 30030

Prime Factorization of 30040

Now multiplying the highest exponent prime factors to calculate the LCM of 30030 and 30040.

LCM(30030,30040) = 2³ × 3¹ × 5¹ × 7¹ × 11¹ × 13¹ × 751¹
LCM(30030,30040) = 90210120