What is the Least Common Multiple of 705 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 705 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 705 and 723, than apply into the LCM equation.

GCF(705,723) = 3
LCM(705,723) = ( 705 × 723) / 3
LCM(705,723) = 509715 / 3
LCM(705,723) = 169905

Least Common Multiple (LCM) of 705 and 723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 705 and 723. First we will calculate the prime factors of 705 and 723.

Prime Factorization of 705

Prime Factorization of 723

Now multiplying the highest exponent prime factors to calculate the LCM of 705 and 723.

LCM(705,723) = 3¹ × 5¹ × 47¹ × 241¹
LCM(705,723) = 169905