Question

Find the least number which when divided by 12,16,18 will leave in each case the same remainder 5

Answer 1

Answer:

149

Step-by-step explanation:

The required least number ( Least Common Multiple ) is

= (L.C.M. of 12 16 and 18 ) + 5

= (2*2*4*3*3)+5 = 144 +5 = 149

Answer 2

Answer:

The least number when divided by 12, 16, and 18, gives a remainder of 3 is 149.

Step-by-step explanation:

We must find

The least number when divided by 12, 16, and 18 should give a remainder of 5.

Let's say the number is N.

Now,

If we subtract 5 from N, we get a number that is divisible by 12, 16, and 18. (Think about it....)

That is, if the remainder is taken away from the Dividend, it becomes divisible by the Divisor.

Now, That number is divisible by 12, 16, and 18, so they have to be the common multiple of these numbers

So, taking LCM,

LCM (12, 16, 18) = 144

So,

144 is the smallest number divisible by 12, 16 and 18.

But our number should be the least and should give 5 as the remainder.

So,

Adding 5 to 144

= 149

Hence,

The least number when divided by 12, 16, and 18, gives a remainder of 5 is 149.

This is true because 144 is divisible by them and adding a five will surely give it a remainder of 5, we can check this by long division.

Hope it helped and believing you understood it....All the best