lcm of two numbers is 120 hcf is 10 .what is the sum of those two numbers

- anonymous

lcm of two numbers is 120 hcf is 10 .what is the sum of those two numbers

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- anonymous

120 and 10

- anonymous

yes

- anonymous

k

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## More answers

- anonymous

65,55

- anonymous

wrong

- ganeshie8

use this, lcm x hcf = product of numbers

- ganeshie8

say the required numbers are x, y
120x10 = xy
xy = 1200 ---------------(1)

- ganeshie8

we're required to find x+y

- anonymous

how

- ganeshie8

thinking, the two numbers can be 10 and 120, thats one possible solution. but thats not wat the question asks here i guess

- ganeshie8

since hcf is 10, x and y must be multiples of 10
x = 10k
y = 10m
substitute these in equaiton (1)

- ganeshie8

xy = 1200
(10k)(10m) = 1200
100km = 1200
km = 12 ---------------(2)

- ganeshie8

now, its easy. coprime factors of 12 :-
3,4

- ganeshie8

so, k = 3, m = 4
that gives x = 30, y = 40

- ganeshie8

sum of numbers is x+y = 30+40 = 70

- ganeshie8

see if that makes some sense

- anonymous

yes i did it in my yesterday exam .i got it but not the proper method

- ganeshie8

good :) so you got the same answer ?

- anonymous

ya

- DebbieG

But why can't it be that so, k = 12, m = 1 that gives x = 120, y = 10??
the product of the uncommon factors is \(\dfrac{LCM}{HCF}=12\)
So the uncommon factors are 2, 2, & 3.... but we can't "split" the 2's because then that would be a common factor, so really 4 & 3 but that would be 4 to one number and 3 to the other, or the 4 and 3 go to the same number so we have 12 to one number and 1 to the other.
I understand what you did above, but I'm not clear on how you can pin the numbers down to 30 & 40 vs. 10 & 120 (unless it said something like, "what is the smallest possible sum of the 2 numbers?).
What am I missing here?

- ganeshie8

see my reply above, attaching the snapshot

##### 1 Attachment

- ganeshie8

when we're given lcm and hcf as 120 and 10, and asked to find both the numbers,
and we come up wid solution as 120 and 10 ? there was nothing we solved when we say both numbers are same as lcm and hcf. eventhough it works, nobody really gets excited wid that solutution :)

- DebbieG

I saw that comment, and I agree that it isn't an "interesting" solution. But I'm talking about the "design" of the problem, I guess.
The problem, as stated, seems to suggest that there is one correct answer, but I don't see how that can be, if we have the whole problem in front of us. As you point out, there is another pair of numbers that works. So we can just say "oh, well, this is what the instructor MEANT to ask.....", and maybe that's all there is to it - in which case, it's a poorly worded question (been there, done THAT, lol).
But if we assume that the problem is asking what it appears to be asking, e.g., what is the ONE and ONLY pair of numbers, then something is missing. Some restriction on the numbers, or something like that.

- ganeshie8

yes that ambiguity is there in this particular problem statement

- DebbieG

So easy to fix, too....
"What is the smallest possible sum of the numbers?"
:)

- ganeshie8

yes i felt the same when i was solving :)

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