Last week, in one lineLowest common multiple — when will they line up again.
Greatest common divisor — what is the largest equal share.
In a word problem, decide which one is being asked before you calculate.
Now you
1Bus A leaves the station every 9 minutes, bus B every 12. They have just left together. After how many minutes do they leave together again?
2In that time, how many buses does A send? And B?
Once you have both numbers, look at them carefully.
3A sheet of paper 24 cm by 36 cm is cut into identical squares with nothing left over. What is the largest possible side, and how many squares are there?
4List every number from 1 to 100 that is a multiple of both 8 and 12.
542 pencils and 28 notebooks are shared equally with nothing left over. What is the greatest number of people, and what does each get?
A little further
6Find the lowest common multiple of 4, 6 and 9.
Three numbers work the same way as two.
7Two whole numbers have greatest common divisor 6 and lowest common multiple 72. Find them. There is more than one answer.
The product of two numbers equals GCD x LCM.
8Check that 'product = GCD x LCM' holds, using 8 and 12.
9Find the greatest common divisor of 84 and 126.
With larger numbers, splitting into prime factors is quicker.
Cutting it up, or tiling it out
10At a station a train leaves every 8 minutes and a bus every 20. They left together at 7 am. Counting 7 am itself, how many times do they leave together before noon?
11Rectangles 18 cm by 30 cm are laid out, all the same way round and with no gaps, to make a square. What is the side of the smallest such square, and how many rectangles does it take?
12Question 3 cut a large sheet into squares; question 11 tiled small sheets into a square. One of them needs the greatest common divisor and the other the lowest common multiple. Which is which, and why?
The important question today. Cutting up, against laying out.
Extra · you may skip thisThree gears (12, 18 and 24 teeth) mesh together. After how many teeth are all three back where they started?