Highest Mutual Ingredient Together With Lowest Mutual Multiple

There are many methods for finding the Highest Common Factor together with Lowest Common Multiple of ii or to a greater extent than numbers.  For years I've been didactics pupils to lay the prime number factors into a Venn Diagram, every bit described here. 

I recently discovered an option method that is impressively quick together with simple.  It is described inwards this video every bit the 'Indian Method'. It's like to the 'upside downwardly birthday cake method' but it's much quicker because in that place is no requirement to role primes.

Say nosotros desire to detect the Highest Common Factor together with Lowest Common Multiple of 24 together with 36.
Write down the ii numbers, then (to the left, every bit inwards my illustration below) write downwardly whatever mutual element (ie 2, 3, 4, vi or 12).  I've chosen 6.  Now dissever 24 together with 36 past times vi together with write the answers underneath (4 together with vi inwards this case).  Keep repeating this procedure until the ii numbers have no mutual factors (ie 2 together with iii below).  Now, your Highest Common Factor is only the production of numbers on the left. And for the Lowest Common Multiple, detect the production of the numbers on the left together with the numbers inwards the bottom row. It's slow to hollo back which is which - to detect the LCM, await for the L shape.

It's thus quick!  And simple!  Try it.

Don Steward features an option method inwards this spider web log post.  He mentions that you lot tin detect a LCM past times dividing the production of the ii numbers past times their HCF ie inwards this example, (24 x 36)/12 = 72.

See my Resources Library for resources for didactics HCF together with LCM.