The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs co
Practice Questions
Q1
The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs could represent these numbers? (2023)
5 and 12
3 and 20
4 and 15
6 and 10
Questions & Step-by-Step Solutions
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.
