What is the smallest number that when divided by 35 and 56?

The question is ambiguous. It could be interpreted in several ways. Here are the most likely interpretations and their solutions:

Interpretation 1: What is the smallest number that is divisible by both 35 and 56?

This interpretation asks for the Least Common Multiple (LCM) of 35 and 56.

Steps to find the LCM:

1. Prime Factorization:

   • 35 = 5 x 7
   • 56 = 2 x 2 x 2 x 7 = 2³ x 7

2. Identify the highest power of each prime factor present in either number:

   • 2³ (from 56)
   • 5 (from 35)
   • 7 (from both 35 and 56)

3. Multiply these highest powers together:

   • LCM (35, 56) = 2³ x 5 x 7 = 8 x 5 x 7 = 280

Answer: The smallest number that is divisible by both 35 and 56 is 280.

Interpretation 2: What is the smallest number that, when divided by 35 and 56, leaves a remainder of 0?

This is essentially the same question as Interpretation 1 and the answer is the same, the LCM.

Answer: The smallest number is 280.

Interpretation 3: What is the smallest number that, when divided by 35 and 56, leaves a specific remainder?

Without a specified remainder, this question is incomplete. If a remainder r was specified, the process would be:

1. Find the LCM of 35 and 56 (which is 280).
2. Add the remainder r to the LCM.

Therefore, the number would be 280 + r.

Conclusion

Based on the most likely interpretations, the smallest number divisible by both 35 and 56 is 280. If a remainder were specified, that remainder would be added to 280.