Question
Find the greatest 3-digit number which when divided by 11
or 16 leaves 3 as remainder.Solution
ATQ,
LCM of 11 and 16 = 176
Let the required number be of the form:
Number = 176 × k + 3
We want the greatest 3-digit number:
176k + 3 ≤ 999
⇒ 176k ≤ 996
⇒ k = 5 (since 176 × 5 = 880)
∴ Required number = 176 × 5 + 3 = 883
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