The total number of fruits, when divided by 2, 3, 4, 5 and 6, leaves the remainders 1, 2, 3, 4 and 5 respectively.
Here (2 – 1) = (3 – 2) = (4 – 3) = (5 – 4) = (6 – 5) = 1.
∴ The required no. of fruits will be LCM (2, 3, 4, 5, 6) – 1
LCM (2, 3, 4, 5, 6) = 2 × 3 × 2 × 5 = 60
Now take the multiples of 60 and subtract 1 from it.
Also checking the conditions, multiplies of 60 are 60, 120, 180, …..
The multiple -1
59, 119, 179, ……
The required number = 119
∴ The total number of fruits = 119.