What is the Least Common Multiple of 1729 and 1749?

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 1729 and 1749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1729 and 1749, than apply into the LCM equation.

GCF(1729,1749) = 1
LCM(1729,1749) = ( 1729 × 1749) / 1
LCM(1729,1749) = 3024021 / 1
LCM(1729,1749) = 3024021

Least Common Multiple (LCM) of 1729 and 1749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1729 and 1749. First we will calculate the prime factors of 1729 and 1749.

Prime Factorization of 1729

Prime Factorization of 1749

Now multiplying the highest exponent prime factors to calculate the LCM of 1729 and 1749.

LCM(1729,1749) = 7¹ × 13¹ × 19¹ × 3¹ × 11¹ × 53¹
LCM(1729,1749) = 3024021