If the HCF of two numbers is 8 and their LCM is 48, what could be one of the pos

If the HCF of two numbers is 8 and their LCM is 48, what could be one of the possible pairs of numbers? (2023)

If the HCF of two numbers is 8 and their LCM is 48, what could be one of the possible pairs of numbers? (2023)

Step 1: Understand that HCF (Highest Common Factor) is the largest number that divides both numbers without leaving a remainder.
Step 2: Understand that LCM (Lowest Common Multiple) is the smallest number that both numbers can divide into without leaving a remainder.
Step 3: Use the relationship between HCF and LCM: HCF × LCM = Product of the two numbers.
Step 4: Substitute the given values: 8 (HCF) × 48 (LCM) = Product of the two numbers.
Step 5: Calculate the product: 8 × 48 = 384.
Step 6: Now, we need to find two numbers that multiply to 384 and have an HCF of 8.
Step 7: Start by dividing 384 by 8 to simplify: 384 ÷ 8 = 48.
Step 8: Now, we need to find two numbers that multiply to 48 and have an HCF of 1 (since we already took out the HCF of 8).
Step 9: Possible pairs of numbers that multiply to 48 are (1, 48), (2, 24), (3, 16), (4, 12), (6, 8).
Step 10: Check which pairs have an HCF of 1: (3, 16) has an HCF of 1.
Step 11: Multiply the pair (3, 16) by the HCF (8) to get the original numbers: 3 × 8 = 24 and 16 × 8 = 128.
Step 12: Therefore, one possible pair of numbers is 24 and 128.

HCF and LCM – Understanding the relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers, specifically that the product of the HCF and LCM equals the product of the two numbers.