What is the Least Common Multiple of 65408 and 65414?

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 65408 and 65414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65408 and 65414, than apply into the LCM equation.

GCF(65408,65414) = 2
LCM(65408,65414) = ( 65408 × 65414) / 2
LCM(65408,65414) = 4278598912 / 2
LCM(65408,65414) = 2139299456

Least Common Multiple (LCM) of 65408 and 65414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65408 and 65414. First we will calculate the prime factors of 65408 and 65414.

Prime Factorization of 65408

Prime Factorization of 65414

Now multiplying the highest exponent prime factors to calculate the LCM of 65408 and 65414.

LCM(65408,65414) = 2⁷ × 7¹ × 73¹ × 32707¹
LCM(65408,65414) = 2139299456