Greatest common factors and least common multiples GCSE exam question

Question

Amber wants to tile her bathroom. It measures 1.2m by 2.16m. She finds square tiles with side length 10cm, 12cm or 18cm. Which of these tiles will fit the wall exactly?

How can I use GCF and LCM to work this out?

1.2 * 2.16 = 2.592 but I dont know what to do next

Thank You and help is appreciated

score 2 · Answer 1 · answered May 28 '19 at 13:25

2

You do not need GCD or LCM at all here. The tile that will fit is the one whose length evenly divides both the room's dimensions. $10$ cm doesn't divide into $216$ cm (the room length, converted from metres), and neither does $18$ cm divide into $120$ cm (the width), so the tile of $12$ cm fits, with sides of $10$ and $18$ tiles.

answered May 28 '19 at 13:25

Parcly Taxel

103,344

O thank you I didnt realise it was in m – xx_Gcsemathstudent_xx May 28 '19 at 13:26

trancelocation · Accepted Answer · 2019-05-28T13:42:09.517

1

If you are still interested in a solution using GCD:

In order to fit exactly for both walls it is necessary for the side length of a tile to divide the GCD of $120$ and $216$: $$(120,216) = 24 \Rightarrow 12 \mbox{ is the fitting tile side}$$

edited May 28 '19 at 13:42

answered May 28 '19 at 13:35

trancelocation

32,243

i.e. $\ c\mid a,b\iff c\mid \gcd(a,b),\ $ the GCD Universal Property. – Bill Dubuque May 28 '19 at 14:02

Greatest common factors and least common multiples GCSE exam question

2 Answers2