What is the Least Common Multiple of 1678 and 1684?

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 1684 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 1684, than apply into the LCM equation.

GCF(1678,1684) = 2
LCM(1678,1684) = ( 1678 × 1684) / 2
LCM(1678,1684) = 2825752 / 2
LCM(1678,1684) = 1412876

Least Common Multiple (LCM) of 1678 and 1684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1678 and 1684. First we will calculate the prime factors of 1678 and 1684.

Prime Factorization of 1678

Prime Factorization of 1684

Now multiplying the highest exponent prime factors to calculate the LCM of 1678 and 1684.

LCM(1678,1684) = 2² × 839¹ × 421¹
LCM(1678,1684) = 1412876