What is the Least Common Multiple of 1749 and 1761?

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 1761 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 1761, than apply into the LCM equation.

GCF(1749,1761) = 3
LCM(1749,1761) = ( 1749 × 1761) / 3
LCM(1749,1761) = 3079989 / 3
LCM(1749,1761) = 1026663

Least Common Multiple (LCM) of 1749 and 1761 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1749 and 1761. First we will calculate the prime factors of 1749 and 1761.

Prime Factorization of 1749

Prime Factorization of 1761

Now multiplying the highest exponent prime factors to calculate the LCM of 1749 and 1761.

LCM(1749,1761) = 3¹ × 11¹ × 53¹ × 587¹
LCM(1749,1761) = 1026663