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 $2520$.

$\blacksquare$

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Ladies' Diary or Woman's Almanac, $\text {1704}$ – $\text {1841}$: $140$