What is the Least Common Multiple of 41993 and 42000?

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 41993 and 42000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 41993 and 42000, than apply into the LCM equation.

GCF(41993,42000) = 7
LCM(41993,42000) = ( 41993 × 42000) / 7
LCM(41993,42000) = 1763706000 / 7
LCM(41993,42000) = 251958000

Least Common Multiple (LCM) of 41993 and 42000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 41993 and 42000. First we will calculate the prime factors of 41993 and 42000.

Prime Factorization of 41993

Prime Factorization of 42000

Now multiplying the highest exponent prime factors to calculate the LCM of 41993 and 42000.

LCM(41993,42000) = 7² × 857¹ × 2⁴ × 3¹ × 5³
LCM(41993,42000) = 251958000