The LCM of two positive integers is twice the larger number. The difference of the smaller number and the HCF of the two numbers is 4. The smaller number is [SSC (10+2)2012] |
A) 12
B) 6
C) 8
D) 10
Correct Answer: C
Solution :
Let the numbers be ax and\[bx,\] where \[x\] is the HCF and \[bx>ax.\] |
\[\therefore \] \[\text{LCM}=abx\] |
\[abx=2bx\]\[\Rightarrow \]\[a=2\] |
Again, \[ax-x=4\] |
On putting the value of ax, we get |
\[2x-x=4\]\[\Rightarrow \]\[x=4\] |
\[\therefore \]Smaller number \[=ax=2\times 4=8\] |
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