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?

Update:

Where's the 4 of (n+4) come from?

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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.

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