What is the Least Common Multiple of 53760 and 53775?

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 53760 and 53775 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 53760 and 53775, than apply into the LCM equation.

GCF(53760,53775) = 15
LCM(53760,53775) = ( 53760 × 53775) / 15
LCM(53760,53775) = 2890944000 / 15
LCM(53760,53775) = 192729600

Least Common Multiple (LCM) of 53760 and 53775 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 53760 and 53775. First we will calculate the prime factors of 53760 and 53775.

Prime Factorization of 53760

Prime Factorization of 53775

Now multiplying the highest exponent prime factors to calculate the LCM of 53760 and 53775.

LCM(53760,53775) = 2⁹ × 3² × 5² × 7¹ × 239¹
LCM(53760,53775) = 192729600