What is the Least Common Multiple of 714 and 729?

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 714 and 729 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 714 and 729, than apply into the LCM equation.

GCF(714,729) = 3
LCM(714,729) = ( 714 × 729) / 3
LCM(714,729) = 520506 / 3
LCM(714,729) = 173502

Least Common Multiple (LCM) of 714 and 729 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 714 and 729. First we will calculate the prime factors of 714 and 729.

Prime Factorization of 714

Prime Factorization of 729

Now multiplying the highest exponent prime factors to calculate the LCM of 714 and 729.

LCM(714,729) = 2¹ × 3⁶ × 7¹ × 17¹
LCM(714,729) = 173502