If the LCM of two numbers is 84 and their HCF is 7, what is the sum of the two n

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Question: If the LCM of two numbers is 84 and their HCF is 7, what is the sum of the two numbers if one of them is 21? (2023)

Options:

Correct Answer: 63

Exam Year: 2023

Solution:

Let the other number be x. Then, 84 = (21 * x) / 7. Solving gives x = 28. The sum is 21 + 28 = 49.

If the LCM of two numbers is 84 and their HCF is 7, what is the sum of the two numbers if one of them is 21? (2023)

If the LCM of two numbers is 84 and their HCF is 7, what is the sum of the two numbers if one of them is 21? (2023)

Step 1: Understand the problem. We have two numbers, one of them is 21, and we need to find the other number.
Step 2: Recall the relationship between LCM (Least Common Multiple), HCF (Highest Common Factor), and the two numbers. The formula is: LCM * HCF = Number1 * Number2.
Step 3: Substitute the known values into the formula. We know LCM is 84 and HCF is 7, so we write: 84 * 7 = 21 * x.
Step 4: Calculate 84 * 7. This equals 588.
Step 5: Now we have the equation: 588 = 21 * x.
Step 6: To find x, divide both sides of the equation by 21: x = 588 / 21.
Step 7: Calculate 588 divided by 21. This equals 28, so x = 28.
Step 8: Now we have both numbers: 21 and 28.
Step 9: Find the sum of the two numbers: 21 + 28.
Step 10: Calculate the sum, which is 49.

LCM and HCF Relationship – The relationship between the Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two numbers is given by the formula: LCM(a, b) * HCF(a, b) = a * b.
Algebraic Manipulation – The ability to manipulate equations to isolate variables and solve for unknowns.