A person X wants to distribute some pens among six children A B C D E and F Suppose A gets twice the...........

Math and Mental Ability Simplification

A person X wants to distribute some pens among six children A B C D E and F. Suppose A gets twice the number of pens received by three times that of four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

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Explanation:

Let the number of pens with A be the LCM of 2, 3, 4, 5, and 6 = 60
Then the number of pens with B = 60/2 = 30
The number of pens with C = 60/3 = 20
The number of pens with D = 60/4 = 15 (an odd number)
The number of pens with E = 60/5 = 12
The number of pens with F = 60/6 = 10
To ensure that all get an even number of pens, we need to double the number of pens bought by A, i.e. 60 × 2 = 120
So, total number of pens bought by X = 120 + 60 + 40 + 30 + 24 + 20 = 294