Question

2. Find the smallest number which, when divided by 12 and 18 leaves remainder 3 in each
case.
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Answer 1

Solution:

12 = 2 x 2 x 3

18 = 2 x 3 x 3

LCM of 12 and 18 = (2)2 x (3)2 = 36

So, The Smallest number is 36 + 3 = 39 which leaves a remainder 3 when divided by 12 and 18.

Answer 2

The smallest number which, when divided by 12 and 18 leaves remainder 3 in each case is 39

Given problem :

Find the smallest number which, when divided by 12 and 18 leaves remainder 3 in each case.

Solution:

To find the smallest number which, when divided by 12 and 18 leaves remainder 3  

we need to find Least common multiple of 12 and 18

LCF(12, 18)

12 = 2 × 2 × 3

18 = 2 × 3 × 3  

LCM (12, 18) = 2 × 2 × 3 × 3 = 36

The Smallest number which perfectly divisible by 12 and 18 is 36    

The remainder when 36 is divisible by 12 and 18 is 0

Here, if we add 3 to 36 = 36 + 3 = 39

The remainder when 39 is divisible by 12 and 18 will be equal to 3  

Therefore,

The smallest number which, when divided by 12 and 18 leaves remainder 3 in each case is 39

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