What is the Least Common Multiple of 57744 and 57760?

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 57760 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 57760, than apply into the LCM equation.

GCF(57744,57760) = 16
LCM(57744,57760) = ( 57744 × 57760) / 16
LCM(57744,57760) = 3335293440 / 16
LCM(57744,57760) = 208455840

Least Common Multiple (LCM) of 57744 and 57760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57744 and 57760. First we will calculate the prime factors of 57744 and 57760.

Prime Factorization of 57744

Prime Factorization of 57760

Now multiplying the highest exponent prime factors to calculate the LCM of 57744 and 57760.

LCM(57744,57760) = 2⁵ × 3² × 401¹ × 5¹ × 19²
LCM(57744,57760) = 208455840