What is the Least Common Multiple of 838 and 854?

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 838 and 854 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 838 and 854, than apply into the LCM equation.

GCF(838,854) = 2
LCM(838,854) = ( 838 × 854) / 2
LCM(838,854) = 715652 / 2
LCM(838,854) = 357826

Least Common Multiple (LCM) of 838 and 854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 838 and 854. First we will calculate the prime factors of 838 and 854.

Prime Factorization of 838

Prime Factorization of 854

Now multiplying the highest exponent prime factors to calculate the LCM of 838 and 854.

LCM(838,854) = 2¹ × 419¹ × 7¹ × 61¹
LCM(838,854) = 357826