Question

Question: Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.

Answer 1

Here , we are asked to find the smallest number which leaves some remainders when divided by certain numbers.
To find the smallest number , follow these steps :-

1) Subtract the remainders from the given numbers:
28-8 = 20
32 -12 = 20

Both of them give 20

2) Find the LCM of 28 and 32
28 = 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2

LCM = 2 × 2 × 2 × 2 × 2 × 7 = 224


3) Smallest no: which leaves remainder 8 and 12 when divided by 28 and 32 = LCM -20 = 224 - 20 = 204

204 is the answer