What is the Least Common Multiple of 66993 and 67008?

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 66993 and 67008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66993 and 67008, than apply into the LCM equation.

GCF(66993,67008) = 3
LCM(66993,67008) = ( 66993 × 67008) / 3
LCM(66993,67008) = 4489066944 / 3
LCM(66993,67008) = 1496355648

Least Common Multiple (LCM) of 66993 and 67008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 66993 and 67008. First we will calculate the prime factors of 66993 and 67008.

Prime Factorization of 66993

Prime Factorization of 67008

Now multiplying the highest exponent prime factors to calculate the LCM of 66993 and 67008.

LCM(66993,67008) = 3¹ × 137¹ × 163¹ × 2⁶ × 349¹
LCM(66993,67008) = 1496355648