What is the Least Common Multiple of 17760 and 17775?

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 17760 and 17775 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17760 and 17775, than apply into the LCM equation.

GCF(17760,17775) = 15
LCM(17760,17775) = ( 17760 × 17775) / 15
LCM(17760,17775) = 315684000 / 15
LCM(17760,17775) = 21045600

Least Common Multiple (LCM) of 17760 and 17775 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17760 and 17775. First we will calculate the prime factors of 17760 and 17775.

Prime Factorization of 17760

Prime Factorization of 17775

Now multiplying the highest exponent prime factors to calculate the LCM of 17760 and 17775.

LCM(17760,17775) = 2⁵ × 3² × 5² × 37¹ × 79¹
LCM(17760,17775) = 21045600