Question
Find the largest four-digit number which when divided
by 8, 9, 11, and 12, leaves a remainder 3, 4, 6, and 7 respectively.Solution
Here we can see that the difference (5) between numbers and remainder is same along all four numbers. 8 = 2³
9 = 3²
11 = 11¹
12 = 2² × 3¹ LCM of (8, 9, 11, 12) = 2³ × 3² × 11
= 8 × 9 × 11
= 792 Largest four-digit number which is a multiple of 792 = 9,504 So, the required number = 9504 − 5 = 9,499
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