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------------------------------------------------ Find the HCF and LCM of 18 and 63. Verify that their product is equal to the product of the given numbers.

A. HCF = 9, LCM = 126, Product = 2268
B. HCF = 6, LCM = 126, Product = 1134
C. HCF = 9, LCM = 126, Product = 1134
D. HCF = 6, LCM = 126, Product = 2268

To find the HCF (Highest Common Factor) of 18 and 63, we need to find the largest number that divides both 18 and 63. The prime factorization of 18 is 2 * 3^2, and the prime factorization of 63 is 3^2 * 7. The common factors are 3^2, which is 9. Therefore, the HCF of 18 and 63 is 9. To find the LCM (Least Common Multiple), we need to find the smallest number that is divisible by both 18 and 63. The prime factorization of 18 is 2 * 3^2, and the prime factorization of 63 is 3^2 * 7. The LCM is the product of the highest powers of all the prime factors involved, so the LCM of 18 and 63 is 2 * 3^2 * 7, which is equal to 126. To verify that their product is equal to the product of the given numbers, we multiply the HCF and LCM: 9 * 126 = 1134.

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