What is the Least Common Multiple of 704 and 723?

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 704 and 723 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 704 and 723, than apply into the LCM equation.

GCF(704,723) = 1
LCM(704,723) = ( 704 × 723) / 1
LCM(704,723) = 508992 / 1
LCM(704,723) = 508992

Least Common Multiple (LCM) of 704 and 723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 704 and 723. First we will calculate the prime factors of 704 and 723.

Prime Factorization of 704

Prime Factorization of 723

Now multiplying the highest exponent prime factors to calculate the LCM of 704 and 723.

LCM(704,723) = 2⁶ × 11¹ × 3¹ × 241¹
LCM(704,723) = 508992