Question
Find the largest four-digit number which when divided
by 5, 7, 9, and 12, leaves a remainder 2, 4, 6, and 9 respectively.Solution
Here we can see that the difference (3) between numbers and remainder is same along all four numbers. 5 = 5¹
7 = 7¹
9 = 3²
12 = 2² × 3¹ LCM of (5, 7, 9, 12) = 2² × 3² × 5 × 7
= 4 × 9 × 5 × 7
= 1260 Largest four-digit number which is a multiple of 1260 = 8,820 So, the required number = 8820 − 3 = 8,817
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