The LCM of two numbers is 84 and their HCF is 12. What are the two numbers? (202
Practice Questions
Q1
The LCM of two numbers is 84 and their HCF is 12. What are the two numbers? (2023)
24 and 42
12 and 84
28 and 36
21 and 48
Questions & Step-by-Step Solutions
The LCM of two numbers is 84 and their HCF is 12. What are the two numbers? (2023)
Step 1: Understand that the LCM (Least Common Multiple) of two numbers is 84 and their HCF (Highest Common Factor) is 12.
Step 2: Let the two numbers be represented as 12x and 12y, where x and y are some integers.
Step 3: Use the formula for LCM: LCM(12x, 12y) = 12 * LCM(x, y).
Step 4: Since we know LCM(12x, 12y) = 84, we can set up the equation: 12 * LCM(x, y) = 84.
Step 5: Divide both sides of the equation by 12 to find LCM(x, y): LCM(x, y) = 84 / 12 = 7.
Step 6: Now, we need to find pairs of integers (x, y) such that their LCM is 7.
Step 7: The pairs (x, y) that satisfy LCM(x, y) = 7 are (1, 7) and (7, 1), but we also have (3, 4) and (4, 3) since 3 and 4 are coprime.
Step 8: Calculate the actual numbers using the pairs: For (3, 4), the numbers are 12*3 = 36 and 12*4 = 48. For (4, 3), the numbers are 12*4 = 48 and 12*3 = 36.
Step 9: The two numbers are 36 and 48, or 48 and 36, which are the same numbers.
