What is the Least Common Multiple of 1678 and 1696?

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 1678 and 1696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1678 and 1696, than apply into the LCM equation.

GCF(1678,1696) = 2
LCM(1678,1696) = ( 1678 × 1696) / 2
LCM(1678,1696) = 2845888 / 2
LCM(1678,1696) = 1422944

Least Common Multiple (LCM) of 1678 and 1696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1678 and 1696. First we will calculate the prime factors of 1678 and 1696.

Prime Factorization of 1678

Prime Factorization of 1696

Now multiplying the highest exponent prime factors to calculate the LCM of 1678 and 1696.

LCM(1678,1696) = 2⁵ × 839¹ × 53¹
LCM(1678,1696) = 1422944