What is the Least Common Multiple of 59040 and 59049?

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 59040 and 59049 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 59040 and 59049, than apply into the LCM equation.

GCF(59040,59049) = 9
LCM(59040,59049) = ( 59040 × 59049) / 9
LCM(59040,59049) = 3486252960 / 9
LCM(59040,59049) = 387361440

Least Common Multiple (LCM) of 59040 and 59049 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 59040 and 59049. First we will calculate the prime factors of 59040 and 59049.

Prime Factorization of 59040

Prime Factorization of 59049

Now multiplying the highest exponent prime factors to calculate the LCM of 59040 and 59049.

LCM(59040,59049) = 2⁵ × 3¹⁰ × 5¹ × 41¹
LCM(59040,59049) = 387361440