What is the Least Common Multiple of 57744 and 57762?

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 57744 and 57762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57744 and 57762, than apply into the LCM equation.

GCF(57744,57762) = 18
LCM(57744,57762) = ( 57744 × 57762) / 18
LCM(57744,57762) = 3335408928 / 18
LCM(57744,57762) = 185300496

Least Common Multiple (LCM) of 57744 and 57762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57744 and 57762. First we will calculate the prime factors of 57744 and 57762.

Prime Factorization of 57744

Prime Factorization of 57762

Now multiplying the highest exponent prime factors to calculate the LCM of 57744 and 57762.

LCM(57744,57762) = 2⁴ × 3² × 401¹ × 3209¹
LCM(57744,57762) = 185300496