Question

(1). There are always 4 bars of chocolates,

left when box of chocolates shared
equally among 8, 10, or 12 children.
Find the smallest number of chocolates
in the box,​

Answer 1

The smallest number of chocolates in the box is 124.

Explanation:

There are always 4 bars of chocolates left in the box when they are share equally among 8, 10, or 12 children.

This means that the smallest number of chocolates in the box is 4 added to the least common multiple of 8, 10 and 12.

LCM(8,10,12).

We factore them by prime factors until all are 1. So

8 - 10 - 12|2

4 - 5 - 6|2

2 - 5 - 3|2

1 - 5 - 3|3

1 - 5 - 1|5

1 - 1 - 1

So

lcm(8,10,12) = 2*2*2*3*5 = 8*15 = 120

Adding 4: 120 + 4 = 124

The smallest number of chocolates in the box is 124.