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The least number, which when divided by 4, 5 and 6 leaves remainder 1, 2 and 3 respectively, is
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- 57
- 59
- 61
- 63
Correct Option: A
We know that when a number is divided by a, b or c leaving remainders p, q or r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a, b and c .
Here t = 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3
∴ The required number = k - t = LCM of ( 4, 5, 6 ) – 3
Hence , The required number = 60 – 3 = 57
