The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs co

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Question: The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs could represent these numbers? (2023)

Options:

Correct Answer: 5 and 12

Exam Year: 2023

Solution:

The pair 5 and 12 has an HCF of 1 and an LCM of 60.

The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs could represent these numbers? (2023)

The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs could represent these numbers? (2023)

Step 1: Understand that HCF (Highest Common Factor) of two numbers is 1, which means the numbers are co-prime (they have no common factors other than 1).
Step 2: Understand that LCM (Lowest Common Multiple) of two numbers is 60, which means the smallest number that both numbers can divide into evenly is 60.
Step 3: To find pairs of numbers that meet these criteria, we need to find two numbers that multiply together to give 60 (since HCF is 1, their product is equal to their LCM).
Step 4: List the pairs of factors of 60: (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10).
Step 5: Check each pair to see if they have an HCF of 1: (1, 60) -> HCF is 1, (2, 30) -> HCF is 2, (3, 20) -> HCF is 1, (4, 15) -> HCF is 1, (5, 12) -> HCF is 1, (6, 10) -> HCF is 2.
Step 6: The pairs that have an HCF of 1 are (1, 60), (3, 20), (4, 15), and (5, 12).
Step 7: Verify the LCM of the valid pairs: LCM(1, 60) = 60, LCM(3, 20) = 60, LCM(4, 15) = 60, LCM(5, 12) = 60.
Step 8: Since all these pairs have an LCM of 60 and an HCF of 1, the pair 5 and 12 is one of the valid pairs.

HCF and LCM – Understanding the relationship between the highest common factor (HCF) and the least common multiple (LCM) of two numbers, particularly that HCF * LCM = product of the two numbers.
Co-prime Numbers – Recognizing that if the HCF of two numbers is 1, they are co-prime, meaning they have no common factors other than 1.