Question

Find the smallest 4-digit number which can be exactly divisible by 20, 24 and 30.

Answer 1

Step-by-step explanation:

The smallest 4-digit =1000

Now L.C.M of 12,15,20and35

2∣12,15,20,35

2∣6,15,20,35

3∣15,5,35

5∣1,5,5,35

7∣1,1,1,1

  1,1,1,1

L.C.M.=2×2×3×5×7=420

We divided 1000 by 420

420)1000(2

−840

160−Remainder

∴ The least 4−digit number that is exactly divisible by 12,15,20 and 35

=1000+(420−160)

=1000+260=1,260