helen asked in 科學及數學數學 · 1 decade ago

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?

2 Answers

Rating
  • 1 decade ago
    Favorite Answer

    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.

  • Auntie
    Lv 5
    1 decade ago

    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

Still have questions? Get your answers by asking now.