Question
Find the largest four-digit number which when divided
by 7, 13, 14, and 20, leaves a remainder 1, 7, 8, and 14 respectively.Solution
Here we can see that the difference (6) between numbers and remainder is same along all four numbers. 7 = 7¹
13 = 13¹
14 = 2 × 7
20 = 2² × 5 LCM of (7, 13, 14, 20) = 2² × 5 × 7 × 13
= 4 × 5 × 7 × 13
= 1820 Largest four-digit number which is a multiple of 1820 = 9,100 So, the required number = 9100 − 6 = 9,094
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