Question
Let ‘y’ be the smallest number divisible by 12, 20,
28, and 42, such that ‘y’ is a perfect square. What will be the remainder when ‘y’ is divided by 97?Solution
Prime factors 12 = 2² × 3 20 = 2² × 5 28 = 2² × 7 42 = 2 × 3 × 7 LCM LCM = 2² × 3 × 5 × 7 = 420 Make it a perfect square 420 = 2² × 3¹ × 5¹ × 7¹ → need to multiply by 3 × 5 × 7 = 105 → y = 420 × 105 = 44100 = 210² Find remainder when divided by 97 210 ≡ 16 (mod 97) So y = 210² ≡ 16² = 256 ≡ 62 (mod 97) Final Answer: 62
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