Question

A number less than 500, when divided by 4,5,6,7 leaves remainder 1 in each case. The number is
a)211
b)420
c)421
d)441​

Answer 1

The number is 421

Given :

A number less than 500, when divided by 4 , 5 , 6 , 7 leaves remainder 1 in each case

To find :

The number is

a) 211

b) 420

c) 421

d) 441

Solution :

Step 1 of 2 :

Find LCM of the numbers

Here the given numbers are 4 , 5 , 6 , 7

4 = 2 × 2

5

6 = 2 × 3

7

So the LCM of 4 , 5 , 6 , 7

= 2 × 2 × 3 × 5 × 7

= 420

Step 2 of 2 :

Find the number

Since the number is less than 500 and when divided by 4 , 5 , 6 , 7 leaves remainder 1 in each case

Thus the required number

= 420 + 1

= 421

Hence the correct option is c) 421

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