Question
Find the largest four-digit number which when divided
by 9, 12, 16, and 18, leaves a remainder 2, 5, 9, and 11 respectively.Solution
Here we can see that the difference (7) between numbers and remainder is same along all four numbers. 9 = 3²
12 = 2² × 3
16 = 2⁴
18 = 2 × 3² LCM of (9, 12, 16, 18) = 2⁴ × 3²
= 16 × 9
= 144 Largest four-digit number which is a multiple of 144 = 9,936 So, the required number = 9936 − 7 = 9,929
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