What is the Least Common Multiple of 34 and 104?

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 34 and 104 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 104, than apply into the LCM equation.

GCF(34,104) = 2
LCM(34,104) = ( 34 × 104) / 2
LCM(34,104) = 3536 / 2
LCM(34,104) = 1768

Least Common Multiple (LCM) of 34 and 104 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 104. First we will calculate the prime factors of 34 and 104.

Prime Factorization of 34

Prime Factorization of 104

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 104.

LCM(34,104) = 2³ × 17¹ × 13¹
LCM(34,104) = 1768