What is the Least Common Multiple of 65760 and 65780?

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 65760 and 65780 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65760 and 65780, than apply into the LCM equation.

GCF(65760,65780) = 20
LCM(65760,65780) = ( 65760 × 65780) / 20
LCM(65760,65780) = 4325692800 / 20
LCM(65760,65780) = 216284640

Least Common Multiple (LCM) of 65760 and 65780 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65760 and 65780. First we will calculate the prime factors of 65760 and 65780.

Prime Factorization of 65760

Prime Factorization of 65780

Now multiplying the highest exponent prime factors to calculate the LCM of 65760 and 65780.

LCM(65760,65780) = 2⁵ × 3¹ × 5¹ × 137¹ × 11¹ × 13¹ × 23¹
LCM(65760,65780) = 216284640