Number Theory

Choose the Correct Answer

Correct Answer : Option a

Explanation
Let the number of notebooks each child receives be:
P = 3Q = 4R = 6S = 2T = 5U
To find the minimum value of P such that Q, R, S, T, U are all integers and each receives an even number, we find the LCM of the denominators in the expressions for Q, R, S, T, and U:
P=LCM (3,4,6,2,5) = 60k
To make all values even, choose the smallest even multiplier of 60 that ensures even values for Q = P/3, R = P/4, etc.
Try P = 120
Q = 120/3 = 40
R = 120/4 = 30
S = 120/6 = 20
T = 120/2 = 60
U = 120/5 = 24
Q = 40, R = 30, S = 20, T = 60, U = 24 → all even
Now total notebooks = P + Q + R + S + T + U = 294
Thus, the minimum number of notebooks = 294
Hence, option a is correct.