Question

Find the least fiumber. which is divided by 14,17,20.
leaves the remainder
2, 3, 4 respectively.​

Answer 1

Common difference between divisors and respective remainders

= (2 – 1) = (3 – 2) = (4 – 3) = (5 – 4) = ( 6 – 5) =

1 LCM of (2, 3, 4, 5, 6) = 60 ∴

Required number = 60 k – 1

Now we have to find the least value of k for which 60k – 1 is divisible by 7.

By inspection, we find that for k = 2, 4 × 2 – 1 = 7

∴ Required number = 60 × 2 – 1 = 120 – 1 = 119.