what's the smallest number divisible by all numbers 1-11?

Question

What’s the SMALLEST number that is divisible by ALL of the numbers from 1 to 11? Explain how you know.

Answer 1

Since the integer number n needs to be the smallest integer (positive) divisible by all numbers from 1 to 11 it must have the decomposition n=(2^3)(3^2)(5)(7)(11). This follows from the fundamental theorem of arithmetic. You just need to look at the number 2(3)(4)(5)(6)(7)(8)(9)(10)11 and keep only sufficiently many of them.