find the least 5-digit number which on dividing by 4,12,20 and 24 leaves remainder 3 in each case

We have to find a 5 digit number which on dividing by 4,12,20 and 24 leaves remainder 3 in each case.

So,

LCM(4,12,20,24) = 120

So to obtain a five digit number we have to multiply the LCM by 84.

Therefore the required number 

= 10080 + 3

= 10083

  • 5

Lcm of 4,12, 20 and 24 is

2

04

12

20

24

2

2

6

10

12

3

1

3

5

6

2

1

1

5

2

5

1

1

5

1

1

1

1

1

Lcm= 2x2x3x2x5= 120

Remainder is 3. Hence, 120+3= 123

Hence, 123 is smallest 3 digit no

But U want 5 digit hence, 120x84= 10080 is Lcm

And remainder should be 3 so required answer is 10083

Please vote if helpful!!!

  • 5
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