question_answer

The difference of L.C.M. and H.C.F. of the numbers 40,240 and 480 is equal to twice a number. Find the number.

A)  340                                       

B)  440

C)  220                       

D)              880

Correct Answer: C

Solution :

    L.C.M. of 40, 240 and 480 \[=2\times 2\times 2\times 2\times 2\times 3\times 480\] To find H.C.F. of 40, 240, 480 \[40=2\times 2\times 2\times 5\] \[240=2\,\times 2\times 2\times 2\times 3\times 5\] \[480=2\times 2\times 2\times 2\times 2\times 3\times 5\] H.C.F. of 40, 240 and 480 \[=2\times 2\times 2\times 5=40\] Difference of L.C.M. and H.C.F. = 480 - 40 = 440 Let the required number be x then given 440 = 2x or \[x=\frac{440}{2}=220\]