What is the Least Common Multiple of 27730 and 27744?

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 27730 and 27744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27730 and 27744, than apply into the LCM equation.

GCF(27730,27744) = 2
LCM(27730,27744) = ( 27730 × 27744) / 2
LCM(27730,27744) = 769341120 / 2
LCM(27730,27744) = 384670560

Least Common Multiple (LCM) of 27730 and 27744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27730 and 27744. First we will calculate the prime factors of 27730 and 27744.

Prime Factorization of 27730

Prime Factorization of 27744

Now multiplying the highest exponent prime factors to calculate the LCM of 27730 and 27744.

LCM(27730,27744) = 2⁵ × 5¹ × 47¹ × 59¹ × 3¹ × 17²
LCM(27730,27744) = 384670560