Sunday Times Teaser 2853 – Marble Marvel

by Mike Fletcher

Published May 28 2017 (link)

I had a cuboid (or rectangular block) of marble whose volume in cubic centimetres was divisible by each of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. Unfortunately I dropped the block and it broke into two cuboids, and surprisingly the two new blocks were of similar shape to each other (ie, one was a magnification of the other). The lengths of the sides of the original block and the two new blocks were all two-figure numbers of centimetres.

What were the lengths of the sides of the original block?