F.1 Maths

When a number is divided by 6, the remainder is 2. When it is divided by 9, the remainder is 5 and the remainder is 11 when divided by 15. What is the least value of this number?

Let the least value of this number be n.

(n + 4) is the smallest number which can be divisible by 6, 9 and 15.
Therefore, (n + 4) is the L.C.M. of 6, 9 and 15.

6 = 2 x 3
9 = 3 x 3
15 = 3 x 5

n + 4
= L.C.M. of 6, 9 and 11
= 2 x 3 x 3 x 5
= 90

n + 4 = 90
n = 86

The least value of this number = 86 .

2009-08-12 15:14:59 補充：
When n is divided by 6, the remainder is 2.
2 + 4 = 6
Then n + 4 is divisible by 6.

When n is divided by 9, the remainder is 5.
5 + 4 = 9
Then n + 4 is divisible by 9.

When n is divided by 15, the remainder is 11.
11 + 4 = 15
Then n + 4 is divisible by 15.

2009-08-12 15:15:25 補充：
When n is divided by 6, the remainder is 2.
2 + 4 = 6
Then n + 4 is divisible by 6.

When n is divided by 9, the remainder is 5.
5 + 4 = 9
Then n + 4 is divisible by 9.

When n is divided by 15, the remainder is 11.
11 + 4 = 15
Then n + 4 is divisible by 15.

If 4 is added to this number, then it can be divided by 6, 9, 15 without remainder.

The LCM of 6, 9, 15 is 90

So the least value of this number is 90 - 4 = 86