What is the Least Common Multiple of 67704 and 67724?

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 67704 and 67724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67704 and 67724, than apply into the LCM equation.

GCF(67704,67724) = 4
LCM(67704,67724) = ( 67704 × 67724) / 4
LCM(67704,67724) = 4585185696 / 4
LCM(67704,67724) = 1146296424

Least Common Multiple (LCM) of 67704 and 67724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67704 and 67724. First we will calculate the prime factors of 67704 and 67724.

Prime Factorization of 67704

Prime Factorization of 67724

Now multiplying the highest exponent prime factors to calculate the LCM of 67704 and 67724.

LCM(67704,67724) = 2³ × 3¹ × 7¹ × 13¹ × 31¹ × 16931¹
LCM(67704,67724) = 1146296424