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The largest four-digit number which when divided by 9, 18 and 23, leaves a remainder 5 in each case, is:
Question

The largest four-digit number which when divided by 9, 18 and 23, leaves a remainder 5 in each case, is:

A.

9941

B.

9963

C.

9921

D.

9935

Correct option is A

Given:
The required number leaves remainder 5 when divided by 9, 18 and 23.
Formula Used:
Required number = (LCM of divisors × k) + remainder
Solution:
LCM of 9, 18 and 23 = 414
Largest four-digit number ≈ 9999
9999 − 5 = 9994
9994 ÷ 414 = 24
Required number = (414 × 24) + 5 = 9941

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