# Ladies' Diary/Lowest Common Multiple of 1 to 9

## Puzzle

What is the least number which will divide by the nine digits without leaving a remainder?

## Solution

$2520$.

## Proof

This is the same as asking:

What is the lowest common multiple of $\set {1, 2, 3, 4, 5, 6, 7, 8, 9}$?

This must be $5 \times 7 \times 8 \times 9$ which is $2520$.

$\blacksquare$