12 May 2014

Highest Common Factor and Lowest Common Multiple

There are many methods for finding the Highest Common Factor and Lowest Common Multiple of two or more numbers.  For years I've been teaching pupils to put the prime factors into a Venn Diagram, as described here

I recently discovered an alternative method that is impressively quick and simple.  It is described in this video as the 'Indian Method'. It's similar to the 'upside down birthday cake method' but it's much quicker because there is no requirement to use primes.

Say we want to find the Highest Common Factor and Lowest Common Multiple of 24 and 36.
Write down the two numbers, then (to the left, as in my example below) write down any common factor (ie 2, 3, 4, 6 or 12).  I've chosen 6.  Now divide 24 and 36 by 6 and write the answers underneath (4 and 6 in this case).  Keep repeating this process until the two numbers have no common factors (ie 2 and 3 below).  Now, your Highest Common Factor is simply the product of numbers on the left. And for the Lowest Common Multiple, find the product of the numbers on the left and the numbers in the bottom row. It's easy to remember which is which - to find the LCM, look for the L shape.

It's so quick!  And simple!  Try it.

Don Steward features an alternative method in this blog post.  He mentions that you can find a LCM by dividing the product of the two numbers by their HCF ie in this example, (24 x 36)/12 = 72.

See my Resources Library for resources for teaching HCF and LCM.

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