## Puzzle #172: Divisibility by first 13 numbers

I acquired a new book recently (thanks to Suman Saraf) – Problem Solving Strategies in Mathematics. Here is a problem from that book. It is a simple problem for adults, so will request people to show it to their children.

The smallest number that is divisible by the first none counting numbers (i.e. 1,2,3,…,9) is 2,520. What would be the smallest number divisible by the first 13 counting numbers?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy counting!

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### 3 Responses to Puzzle #172: Divisibility by first 13 numbers

1. Abhinav Jain says:

360,360

2. 360360

Solution:
Lets say f(n) is “The smallest number that is divisible by the first n counting numbers”
f(n) = Product of highest prime powers less than n
f(9) = 2520
f(13) = f(9)*11*13

3. 2520*11*13