anonymous
  • anonymous
lcm of two numbers is 120 hcf is 10 .what is the sum of those two numbers
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
120 and 10
anonymous
  • anonymous
yes
anonymous
  • anonymous
k

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anonymous
  • anonymous
65,55
anonymous
  • anonymous
wrong
ganeshie8
  • ganeshie8
use this, lcm x hcf = product of numbers
ganeshie8
  • ganeshie8
say the required numbers are x, y 120x10 = xy xy = 1200 ---------------(1)
ganeshie8
  • ganeshie8
we're required to find x+y
anonymous
  • anonymous
how
ganeshie8
  • 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
  • ganeshie8
since hcf is 10, x and y must be multiples of 10 x = 10k y = 10m substitute these in equaiton (1)
ganeshie8
  • ganeshie8
xy = 1200 (10k)(10m) = 1200 100km = 1200 km = 12 ---------------(2)
ganeshie8
  • ganeshie8
now, its easy. coprime factors of 12 :- 3,4
ganeshie8
  • ganeshie8
so, k = 3, m = 4 that gives x = 30, y = 40
ganeshie8
  • ganeshie8
sum of numbers is x+y = 30+40 = 70
ganeshie8
  • ganeshie8
see if that makes some sense
anonymous
  • anonymous
yes i did it in my yesterday exam .i got it but not the proper method
ganeshie8
  • ganeshie8
good :) so you got the same answer ?
anonymous
  • anonymous
ya
DebbieG
  • 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
  • ganeshie8
see my reply above, attaching the snapshot
1 Attachment
ganeshie8
  • 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
  • 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
  • ganeshie8
yes that ambiguity is there in this particular problem statement
DebbieG
  • DebbieG
So easy to fix, too.... "What is the smallest possible sum of the numbers?" :)
ganeshie8
  • ganeshie8
yes i felt the same when i was solving :)

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