Question
What is the least positive number which leaves
remainders 5, 9, and 12 when divided by 8, 12, and 15 respectively?Solution
Required number x satisfies: x ≡ 5 (mod 8) x ≡ 9 (mod 12) x ≡ 12 (mod 15) So x + 3 is divisible by 8, 12, and 15. LCM of 8, 12, 15 = 120 So x + 3 = 120 x = 117
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