What is the Least Common Multiple of 17408 and 17416?

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 17408 and 17416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17408 and 17416, than apply into the LCM equation.

GCF(17408,17416) = 8
LCM(17408,17416) = ( 17408 × 17416) / 8
LCM(17408,17416) = 303177728 / 8
LCM(17408,17416) = 37897216

Least Common Multiple (LCM) of 17408 and 17416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17408 and 17416. First we will calculate the prime factors of 17408 and 17416.

Prime Factorization of 17408

Prime Factorization of 17416

Now multiplying the highest exponent prime factors to calculate the LCM of 17408 and 17416.

LCM(17408,17416) = 2¹⁰ × 17¹ × 7¹ × 311¹
LCM(17408,17416) = 37897216