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A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is :
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- 1539
- 539
- 359
- 1359
Correct Option: C
We know that when a number is divided by a, b or c leaving remainders p, q and 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 = Divisor – remainder = 1
t = 10 – 9 = 1, 9 – 8 = 1, 8 – 7 = 1
∴ Required number = k - t = (L.C.M. of 10, 9, 8) – 1
Hence , Required number = 360 – 1 = 359
