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Determine the smallest number which when divided by 12,16,20,25 and 30 leaves the same remainder 3 in each case.
Question

Determine the smallest number which when divided by 12,16,20,25 and 30 leaves the same remainder 3 in each case.

A.

1023

B.

1203

C.

1303

D.

1233

Correct option is B

Concept used:

When smallest number asked, which when divided by a, b, c leaves the same remainder R in each case, that number is LCM[a, b, c] + R

Solution:

∴ Smallest number which when divided by 12,16, 20.25 and 30 leaves the same remainder 3 in each case is LCM[12,16, 20.25, 30] + 3

= 1200 + 3

= 1203

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