Two numbers have an HCF of 8 and an LCM of 72. If one of the numbers is 16, what

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Question: Two numbers have an HCF of 8 and an LCM of 72. If one of the numbers is 16, what is the other number? (2023)

Options:

Correct Answer: 24

Exam Year: 2023

Solution:

Using the relationship LCM = (Product of the numbers) / HCF, we can find the other number: 72 = (16 * x) / 8, leading to x = 24.

Two numbers have an HCF of 8 and an LCM of 72. If one of the numbers is 16, what is the other number? (2023)

Two numbers have an HCF of 8 and an LCM of 72. If one of the numbers is 16, what is the other number? (2023)

Step 1: Understand the problem. We have two numbers with an HCF (Highest Common Factor) of 8 and an LCM (Lowest Common Multiple) of 72. One of the numbers is 16, and we need to find the other number.
Step 2: Recall the relationship between HCF, LCM, and the two numbers. The formula is: LCM = (Product of the numbers) / HCF.
Step 3: Substitute the known values into the formula. We know the LCM is 72, one number is 16, and the HCF is 8. So, we write: 72 = (16 * x) / 8.
Step 4: Rearrange the equation to solve for x (the other number). Multiply both sides by 8 to eliminate the fraction: 72 * 8 = 16 * x.
Step 5: Calculate 72 * 8, which equals 576. Now we have: 576 = 16 * x.
Step 6: Divide both sides by 16 to find x: x = 576 / 16.
Step 7: Calculate 576 / 16, which equals 36. So, the other number is 36.

HCF and LCM Relationship – Understanding the relationship between Highest Common Factor (HCF) and Lowest Common Multiple (LCM) is crucial for solving problems involving two numbers.
Algebraic Manipulation – The ability to rearrange equations and solve for unknown variables is essential in finding the other number.