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Two numbers have a difference of 14 and their Least Common Multiple (LCM) and Highest Common Factor (HCF) are 441 and 7 respectively. What are the numbers?
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Solution: Step 1: Assume the numbers as 7A and 7B, where A and B are co-prime. Step 2: Given that 7A - 7B = 14, which simplifies to A - B = 2. Step 3: The LCM of the numbers is 7 * A * B = 441, which implies A * B = 63. Step 4: Find the values of A and B that satisfy A - B = 2 and A * B = 63. Step 5: A and B can be 9 and 7 respectively. Step 6: Therefore, the numbers are 7*9 = 63 and 7*7 = 49.
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