What is the Least Common Multiple of 1705 and 1724?

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 1705 and 1724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1705 and 1724, than apply into the LCM equation.

GCF(1705,1724) = 1
LCM(1705,1724) = ( 1705 × 1724) / 1
LCM(1705,1724) = 2939420 / 1
LCM(1705,1724) = 2939420

Least Common Multiple (LCM) of 1705 and 1724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1705 and 1724. First we will calculate the prime factors of 1705 and 1724.

Prime Factorization of 1705

Prime Factorization of 1724

Now multiplying the highest exponent prime factors to calculate the LCM of 1705 and 1724.

LCM(1705,1724) = 5¹ × 11¹ × 31¹ × 2² × 431¹
LCM(1705,1724) = 2939420