How To Find The Two Numbers If The Hcf And Lcm Are Given?

[dsriram2002]

For example, the LCM is 7700 and the HCF is 11?

Please tell me HOW? And how to do it for other numbers....

[factor-fiction]

7700= 7 *11*100 = 7*11*5*5*2*2
Does that help you start this?

[dsriram2002]

ok

[boxtops]

Is this maths homework? This is your second question about HCFs and LCMs. I'm trying hard to remember....

[dsriram2002]

it is not hw, i am in sweden but i am an indian, i am 5th grade here and 6th grade there in india..i am studying the indian 6th grade books. After a month, i am going there and i will be in 7 th grade

[dsriram2002]

now what factor 30?

[bibblebub]

1) write the LCM in terms of its prime factors:- 7700 = 2² x 5² x 7 x 11

2) split those prime factors between a pair of numbers making sure that both have the HCF (also written in terms as its prime factors) in common and at least one of the numbers has the same power as each of primes

e.g. 2² x 5 x 11 and 2 x 5² x 7 x 11

[bibblebub]

sorry that is wrong, they shouldn't have any of the other prime factors in common so

2² x 7 x 11 and 5² x 11

would be ok

[dsriram2002]

boy math is hard didnt understand a thing

[factor-fiction]

I get 1100 and 77 as a solution
You need to work it through.
Have you been taught to use Venn diagrams to solve these?

[boxtops]

Factor, that's new to me, what a good idea to use a Venn diagram for the common factors.

[factor-fiction]

But there will be various solutions. Using Biiblebubs's formula from the other day, the product of the two numbers= LCM x HCF = 7700 x 11= 84700

[dsriram2002]

i have not been i am learning this myself how did you work it out?

[bibblebub]

basically it's all down to the prime factors (apologies for screwing up before)

[factor-fiction]

Start here or find something similar
http://www.schoolworkout.co.uk/ks3work/Factors.htm

[factor-fiction]

This is better

http://www.youtube.com/watch?v=jqhfcejx_NY

[dsriram2002]

oohhh...i know this this is a factor tree

[factor-fiction]

I enjoyed that video.
Unless the numbers are small, always do a factor tree and then a Venn Diagram. As a short cut to find the LCM, if you can find the HCF you can calculate the LCM using the formula bibblebub gave.

The problem in your question (finding two numbers once you know their HCF and LCM) is an unusual one- I don't remember ever seeing that come up in an exam, so I wouldn't worry too much if you can't do this one.

[bert_h]

The example you've given has several different solutions for the two numbers.

Starting from the HCF being 11, let's say one number is 11 * A, and the other is 11 * B, where A and B have NO common factor (because if they did, the HCF would be more than 11, okay?)

So their LCM is 11 * A * B which is given as 7700, therefore A * B = 700.

Now factoring 700 into "co-prime" factors gives us 4 * 7 * 25. You can see that if you split up the 4 between A and B, or the 25, you'd break the condition that A and B are to have no common factor. So the possible answers for A and B are (1) 25 and 28, (2) 7 and 100, (3) 4 and 225, or (4) 1 and 700.

Multiplying by 11, the possible answers to the original question "What two numbers have an HCF of 11 and an LCM of 7700?" are (1) 275 and 308, (2) 77 and 1100, (3) 44 and 2475, or (4) 11 and 7700. The more factors there are in the LCM, the more possible pairs of numbers there would be with the given HCF and LCM.