Maths Homework Help

[rockyracoon]

Please God, can someone help with my daughters homework.

The HCF of 2 numbers is 6. The LCM of the same two numbers is 72.
What are the numbers?

I'm twisted and my head hurts.

Please help :)

[fiction-factory]

Sorry I meant Togo. Do you now agree with 6,72 then J_J?

[Jonathan-Joe]

Fiction - of course I don't agree. The HCF of 6 and 72 is not 2. I've given my answer, take it or leave it, I won't contribute any more to this thread.

[zebo]

I agree now with 6 and 72.
If your daughter takes anything from our efforts, some of whom are or have been, involved in Maths teaching, it should be When all else fails, read the instructions!

[fiction-factory]

And get off your phone while you try to work it out

[fiction-factory]

>Fiction - of course I don't agree. The HCF of 6 and 72 is not 2. I've given my answer, take it or leave it, I won't contribute any more to this thread.

But the HCF given by the OP was 6 not 2

[Jonathan-Joe]

oooops - I keep seeing the figure 2 after HCF. I would now say the two numbers are 6 and 12.

[fiction-factory]

I agree- I misread it too initially. I agree- in an exam/text book the question would have said "The HCF of two numbers is 6..."

[Jonathan-Joe]

No, that's wrong. It is 6 and 72, though it seems a poor question, having to call 72 a multiple of 72.

[Prudie]

Boy am I glad I stayed out of this one :-)

[fiction-factory]

I should clarify, I agree about the wording- but I still disagree with your latest answer of 6 and 12. The LCM of 6 and 12 is 12, not the 72 we need

[fiction-factory]

Sorry J_J - I'm 2 (sorry TWO) minutes " (sorry TOO) late

[fiction-factory]

You should have joined in Prudie- it needed someone to see it with a fresh pair of eyes

[-Talbot-]

I thought about cheating...(my son told me it was 6 and 72 about 1/2 hour ago)

[Psybbo]

Agreed Prudie, I'm none the wiser

[Prudie]

I think it needs to be clear in simple words what these terms mean;
Highest Common Factor is the biggest number that will divide into the two numbers exactly.
Lowest Common Multiple is the smallest number that both the two numbers will divide into exactly.

[sherrardk]

I really dislike these stupid Maths questions that just confuse kids & families (and on line forums). We had a year 7 one about descendants of a woman born in 1914 - nightmare (turns out there was no correct answer, what a swizz - hours of painful 'family' time and then no actual answer).

[jim360]

You could also try 18 and 24 (18*4 = 24*3 = 72)...

which makes me suspect that either whoever wrote the question forgot to check that there wasn't a second answer, or that they are using a (wrong) definition of Least Common Multiple that stops the LCM of two numbers from also being one of those two numbers (ie, that stops 6 and 72 from also being an answer, which it is). Or perhaps you were meant to find both solutions.

[fiction-factory]

Good point, jim360.

[jim360]

Also I figured I'd try and explain the method for solving problems like this:

1. If you are told the LCM (least common multiple) of two numbers, and the highest common factor or the same two numbers, then step 1 is to write the LCM and HCF as products of prime numbers (ie 2,3,5,7,11,13...).

So, here, 6 = 2x3 and 72 = 2x36 = 2x2x18 = 2x2x2x9=2x2x2x3x3 (finding these factorisations is a matter of patience, but basically all you do is check prime numbers in turn to see if they divide the number, so it is doable).

2. Take the factorisation of the LCM, and split off from it the factors from the highest common factor. That's a bit wordy, but what I mean is that you can write that 72 = 2x2x3x(2x3), and 2x3 = 6 as before. Put these factors aside in a second line:

LCF: 6 = 2x3 (Set 1)
LCF out of HCM: 6 = 2x3 (set 2)

left-over factors: 2, 2, 3

3. The exercise now is to arrange what is left such that all prime factors are used up but no more prime numbers are common to the two numbers you end up building. Here this can be achieved in two ways: giving all the left-over factors to Set 2 (the 6 and 72 solution), or giving all remaining 2's to Set 1 and the last 3 to Set 2 (giving 24 and 18).

That explanation really needs a picture to clear up, I fear... I will try and produce one tomorrow, if you like? But hopefully the above can be followed. It's hard to tell as I'm a bit tired right now.

[gness]

Lordy, Jim.....if that's you when you're tired god help us when you're buzzing.....☺