Simple HCF (GCD) and LCM


Learning Objective

  • We are learning to find the HCF (highest common factor) of two numbers
  • We are learning to find the LCM (least common multiple) (lowest common multiple) of two numbers
  • HCF is also known as GCD (greatest common divisor)

Investing:

  • This is useful because the HCF is just the thing to divide by to simplify fractions or simplify ratios.
  • The LCM is just the number to use as a common denominator if you want to add or subtract fractions.
  • A functional (real-life) application is ...
  • This skill leads to factorising algebra.
  • A 'free gift' with this skill is that we can now also...
  • This could help you if you want to work in...

Preparing:

  • Can you already list all the factors of a number such as 12?
  • Can you also list the first ten multiples of 12?
  • Can you reliably remember which is which?!

  • Let's be sure you can spot factors and multiples by playing the multiple and factor chasepuzzle:
    • start at any number in the list
    • choose another number which has not yet been visited and is either a factor or multiple of the last number.
    • say whether it is a factor or multiple of the last one
    • repeat steps 2 and 3 until you get stuck
    • try to keep going as long as you can.
  • Example on a 1 to 6 ring:
multiple-factor_chase.png
Multiple and factor chase on a 1 to 6 ring. A failed attempt!

  • Here is a worksheet that allows you to try it quickly for yourself. Maybe use pencil or even put your worksheets through a plastic laminator so you can write on them with a dry-erase pen. And here are some solutions (don't cheat!)

  • Why not try with other numbers? If you really want a challenge, try the same task with numbers from 1 to 100. Don't try to put them in a ring, just cross them off on a 100 square and write down your best path using the arrow code I've used above. Getting anywhere over 50 crossed off before you get stuck is really good. What's your personal best?

  • Before you start you need to know:
  • You will have a deeper understanding if you also know:

Discovering:

  • Can you figure it out yourself from these examples?
  • Try to predict the next one aloud or on a mini-whiteboard.
  • Investigate...

Modeling:

  • Here are some examples of people getting it right:
  • Here are some examples of people getting it wrong in typical ways:
  • Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

  • What would this one be? Tell your learning partner. Convince them you're right.
  • Explain how you know.
  • How would you explain this to someone who was new to it?

Explaining:

  • One way to do this is...
  • Another approach might be...
  • A useful shortcut is to...
  • This works because...
  • It doesn't work when...
  • An exception is...
  • Watch out for...
  • A common mistake is...
  • You can check your result by...
  • We can prove this works by...

Practicing:

  • Some straightforward examples.
  • Some harder examples.
  • Some mixed examples.
  • Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
  • You can demonstrate fluency by at least...

Sharing:

  • A web page or wiki I have created to explain this can be found at...
  • A presentation I have created and rehearsed looks like...
  • A poster I have drawn or model I have made can be found...

Assessing:

  • Check you've mastered this skill by...
  • Show you understand by explaining...
  • Prove you're an expert in... by...

Developing:

  • Next we could learn...
  • This leads to...
  • Now try...

last edited: Sep 18, 2011 4:54 pm