What is the Least Common Multiple of 65680 and 65696?

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 65680 and 65696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65680 and 65696, than apply into the LCM equation.

GCF(65680,65696) = 16
LCM(65680,65696) = ( 65680 × 65696) / 16
LCM(65680,65696) = 4314913280 / 16
LCM(65680,65696) = 269682080

Least Common Multiple (LCM) of 65680 and 65696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65680 and 65696. First we will calculate the prime factors of 65680 and 65696.

Prime Factorization of 65680

Prime Factorization of 65696

Now multiplying the highest exponent prime factors to calculate the LCM of 65680 and 65696.

LCM(65680,65696) = 2⁵ × 5¹ × 821¹ × 2053¹
LCM(65680,65696) = 269682080