What is the Least Common Multiple of 90496 and 90514?

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 90496 and 90514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90496 and 90514, than apply into the LCM equation.

GCF(90496,90514) = 2
LCM(90496,90514) = ( 90496 × 90514) / 2
LCM(90496,90514) = 8191154944 / 2
LCM(90496,90514) = 4095577472

Least Common Multiple (LCM) of 90496 and 90514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90496 and 90514. First we will calculate the prime factors of 90496 and 90514.

Prime Factorization of 90496

Prime Factorization of 90514

Now multiplying the highest exponent prime factors to calculate the LCM of 90496 and 90514.

LCM(90496,90514) = 2⁷ × 7¹ × 101¹ × 167¹ × 271¹
LCM(90496,90514) = 4095577472