Question

What will be the least number,
which is divided by 3, 4, 6 and 9.
leaves a remainder 2. but when
divided by 11 leaves no remainder.
:itor School. 2006)​

Answer 1

Answer:

110 is the least number.

Explanation:

Let's calculate LCM of 3, 4, 6, 9 = 36

Now multiple of 36 when added to 2 gives you multiple of 11.

Therefore, (36n + 2) is a multiple of 11, where n represents multiple of 36.

Now let's split 36n to the nearest multiple of 11. So the split = 33n + 3n + 2

You can now say that 3n + 2 = 11

⇒ n = (11-2)/3 = 3

The value of n = 3, Let's apply this value to the equation (36n + 2)

⇒ 36*3 + 2

⇒ 108 + 2 = 110