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and yeah going across in number system an excellent problem could be
How many pairs of numbers have their LCM as 23 × 32.
For 23*32
we have 23 as a prime number and hence the number of pairs would depend on the number of factors of 32 i.e 2^5
No. of Factors of 32 = 5+1=6
Therefore there can be 6 pair combinations
23*32
46*16
92*8
184*4
368*2
736*1
Is this correct?
When I let go of what I am, I become what I might be.
How many pairs of numbers have their LCM as 23 × 32.
For 23 * 32
23^1 * 2^5
If one of the number is 23 ×32, the other number can be any factor of it for LCM to be 23 * 32 which means 2*6 = 12 factors. so 12 such pairs.
If neither number is 23 × 32, then one number will be of the form 23 × 2^a and other will be of the form 23^b × 2^5, where a can take values 0 to 4 and b can take value only 0. which means 5 values.
Hence a total of 17 values.
I Hope i am clear.
Last edited by vickykansal; 30-05-2007 at 03:22 PM.
hey.. gave jus a momen's thot to the above LCM q... so jus posting an approach..
for nos having 23 *32 as L.C.M , one of them has to be 23*32 itself.. n the other number shall be any other higher multiple of 23*32...
Higher... Why higher... if they are higher the LCM will change. True one number can be 23 * 32 and the other number can any other smaller number which is a factor of it.
Higher... Why higher... if they are higher the LCM will change. True one number can be 23 * 32 and the other number can any other smaller number which is a factor of it.
dunno wat i was thking.. read it as lcm but all the time had hcf in mind while solving.. extyremekly silly of me
Nothing is too big a deal... ur perspective is...!!
For 23*32
we have 23 as a prime number and hence the number of pairs would depend on the number of factors of 32 i.e 2^5
No. of Factors of 32 = 5+1=6
Therefore there can be 6 pair combinations
23*32
46*16
92*8
184*4
368*2
736*1
Is this correct?
buddy, you r simply halving one and doubling the other..In the process you have preserved the product, not the LCM.......
@vickykansal 23 x 3 : is 23 x 2^5 is correct
so it gives you total factors as 12 and not PAIRS . pairs are 6 and of these pairs only 1 pair i e (23*32) x 1 gives u the LCM as 23 x 32.
eg : consider other pair : 46 x 16(Chicane u can see here how u went wrong). here the LCM is 23 x 2^4 and not the desired 23 x 2^5 .
hope it explains .
now think ahead....
Correction : In my earlier post i meant only 1 pair i e (23*32) x 1 other than 23 x 32 gives u the LCM as 23 x 32. it means of these 6 pairs only 2 pairs will give you LCM as 23 x 32.
Correction : In my earlier post i meant only 1 pair i e (23*32) x 1 other than 23 x 32 gives u the LCM as 23 x 32. it means of these 6 pairs only 2 pairs will give you LCM as 23 x 32.
dint get wat exactly u mean by this... cud u explain wat 2 pairs are u tallkin bout...
howevr after solving , am getting 17 such pairs only in total...du u have a different ans...
Nothing is too big a deal... ur perspective is...!!
Help
...my apologies.
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