What is the Least Common Multiple of 9800 and 9814?

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 9800 and 9814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9800 and 9814, than apply into the LCM equation.

GCF(9800,9814) = 14
LCM(9800,9814) = ( 9800 × 9814) / 14
LCM(9800,9814) = 96177200 / 14
LCM(9800,9814) = 6869800

Least Common Multiple (LCM) of 9800 and 9814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9800 and 9814. First we will calculate the prime factors of 9800 and 9814.

Prime Factorization of 9800

Prime Factorization of 9814

Now multiplying the highest exponent prime factors to calculate the LCM of 9800 and 9814.

LCM(9800,9814) = 2³ × 5² × 7² × 701¹
LCM(9800,9814) = 6869800