What is the Least Common Multiple of 3400 and 3408?

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 3400 and 3408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3400 and 3408, than apply into the LCM equation.

GCF(3400,3408) = 8
LCM(3400,3408) = ( 3400 × 3408) / 8
LCM(3400,3408) = 11587200 / 8
LCM(3400,3408) = 1448400

Least Common Multiple (LCM) of 3400 and 3408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3400 and 3408. First we will calculate the prime factors of 3400 and 3408.

Prime Factorization of 3400

Prime Factorization of 3408

Now multiplying the highest exponent prime factors to calculate the LCM of 3400 and 3408.

LCM(3400,3408) = 2⁴ × 5² × 17¹ × 3¹ × 71¹
LCM(3400,3408) = 1448400