Shortest path: HCF and LCM
Get from one card to another one disk at a time. Two of the shortest paths pass through the HCF and the LCM.
Before this, try: One disk change, one card change
You need: A pack of Prime Colours cards, two blank card mats and coloured counters.
Players: 1 or more
Goal: Find two shortest paths between two numbers, one disk at a time.
Steps
- Pick two cards and build each one with disks on its own mat.
- Change one disk at a time to get from the first number to the second.
- Find a path that only takes disks out until the two mats match, then puts disks in.
- Now find a path that only puts disks in until they match, then takes disks out.
Make the same
Taking disks out until both mats are the same gives the highest common factor: the biggest number made from the colours they share.
Putting disks in until both mats are the same gives the lowest common multiple: the smallest number that contains both sets of colours.
- Which path is shorter? Is it always?
- What happens when the two numbers share no colours?
Get the cards
Every activity here uses a Prime Colours pack. The shop is reopening soon; email to order a pack now.
Staff training & parent workshops
Bring Prime Colours to your school: hands-on sessions for teachers and families.
New activities arrive through the year. Join the newsletter to get them first.