What is the Least Common Multiple of 27744 and 27760?

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 27744 and 27760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27744 and 27760, than apply into the LCM equation.

GCF(27744,27760) = 16
LCM(27744,27760) = ( 27744 × 27760) / 16
LCM(27744,27760) = 770173440 / 16
LCM(27744,27760) = 48135840

Least Common Multiple (LCM) of 27744 and 27760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27744 and 27760. First we will calculate the prime factors of 27744 and 27760.

Prime Factorization of 27744

Prime Factorization of 27760

Now multiplying the highest exponent prime factors to calculate the LCM of 27744 and 27760.

LCM(27744,27760) = 2⁵ × 3¹ × 17² × 5¹ × 347¹
LCM(27744,27760) = 48135840