Positive integers 30, 72, and N have the property that the product of any two of them is divisible by the third. What is the smallest possible value of N?(adsbygoogle = window.adsbygoogle || []).push({});

Note I have not yet taken a Number Theory course.

I think I have found the solution using a bit of reasoning and some luck. N=60? I figured N could not be smaller than the gcd of 30 and 72, and could not be greater than their product. I also found a pattern for (30N)/72. Inputting 10, 15, 20, 30 for N gave a result of 25/6, 25/4, 25/3, 25/2, respectively. I figured that this converged to 25/1, which would then be my solution. N=60 indeed yields 25/1.

However, I feel that this is closer to luck than anything else, and also it is not very elegant. Can someone show me another way of doing this, perhaps something more elegant?

-F

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple Number Theory Problem

Loading...

Similar Threads - Simple Number Theory | Date |
---|---|

I Semi-simple Lie algebra | Mar 10, 2018 |

I Projective Representations: a simple example | Jan 17, 2018 |

Sophie Germain Triangular Numbers: An Explicit (Simple/r) Formula via Pell Numbers | Mar 17, 2011 |

Simple number theory, divisibility | Sep 16, 2009 |

**Physics Forums - The Fusion of Science and Community**