What is the Least Common Multiple of 1749 and 1756?

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 1749 and 1756 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1749 and 1756, than apply into the LCM equation.

GCF(1749,1756) = 1
LCM(1749,1756) = ( 1749 × 1756) / 1
LCM(1749,1756) = 3071244 / 1
LCM(1749,1756) = 3071244

Least Common Multiple (LCM) of 1749 and 1756 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1749 and 1756. First we will calculate the prime factors of 1749 and 1756.

Prime Factorization of 1749

Prime Factorization of 1756

Now multiplying the highest exponent prime factors to calculate the LCM of 1749 and 1756.

LCM(1749,1756) = 3¹ × 11¹ × 53¹ × 2² × 439¹
LCM(1749,1756) = 3071244