What is the Least Common Multiple of 31749 and 31762?

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 31749 and 31762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31749 and 31762, than apply into the LCM equation.

GCF(31749,31762) = 1
LCM(31749,31762) = ( 31749 × 31762) / 1
LCM(31749,31762) = 1008411738 / 1
LCM(31749,31762) = 1008411738

Least Common Multiple (LCM) of 31749 and 31762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31749 and 31762. First we will calculate the prime factors of 31749 and 31762.

Prime Factorization of 31749

Prime Factorization of 31762

Now multiplying the highest exponent prime factors to calculate the LCM of 31749 and 31762.

LCM(31749,31762) = 3¹ × 19¹ × 557¹ × 2¹ × 15881¹
LCM(31749,31762) = 1008411738