Therefore, the smallest number that is divisible by both 306 and 657 is 1581378.
To find the smallest number which is divisible by both 306 and 657, we need to find their least common multiple (LCM).
We can start by finding the prime factorization of each number:
306 = 2 x 3 x 3 x 17
657 = 3 x 3 x 73
To find the LCM, we need to take the highest power of each prime factor that appears in either factorization. That means we need to include the factors 2, 3, 17, and 73, and for each factor we need to take the highest power that appears in either factorization:
2^1 x 3^2 x 17^1 x 73^1 = 1581378