What is the Least Common Multiple of 30039 and 30048?

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 30039 and 30048 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30039 and 30048, than apply into the LCM equation.

GCF(30039,30048) = 3
LCM(30039,30048) = ( 30039 × 30048) / 3
LCM(30039,30048) = 902611872 / 3
LCM(30039,30048) = 300870624

Least Common Multiple (LCM) of 30039 and 30048 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30039 and 30048. First we will calculate the prime factors of 30039 and 30048.

Prime Factorization of 30039

Prime Factorization of 30048

Now multiplying the highest exponent prime factors to calculate the LCM of 30039 and 30048.

LCM(30039,30048) = 3¹ × 17¹ × 19¹ × 31¹ × 2⁵ × 313¹
LCM(30039,30048) = 300870624