If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two

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Question: If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers if one of them is 25?

Options:

Correct Answer: 50

Solution:

Let the other number be x. Then, HCF(25, x) = 5 and LCM(25, x) = 100. Therefore, 25 * x = 5 * 100, which gives x = 20. The sum is 25 + 20 = 45.

If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers if one of them is 25?

If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers if one of them is 25?

Step 1: Identify the given information. We know the HCF (Highest Common Factor) of two numbers is 5, the LCM (Lowest Common Multiple) is 100, and one of the numbers is 25.
Step 2: Let the other number be represented as 'x'.
Step 3: Use the relationship between HCF and LCM. The formula is: HCF(a, b) * LCM(a, b) = a * b. Here, a is 25 and b is x.
Step 4: Substitute the known values into the formula: 5 * 100 = 25 * x.
Step 5: Calculate the left side: 5 * 100 = 500.
Step 6: Now we have the equation: 500 = 25 * x.
Step 7: To find x, divide both sides by 25: x = 500 / 25.
Step 8: Calculate the division: x = 20.
Step 9: Now we have both numbers: 25 and 20.
Step 10: Find the sum of the two numbers: 25 + 20 = 45.

HCF and LCM Relationship – Understanding the relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers, specifically the formula: HCF(a, b) * LCM(a, b) = a * b.
Properties of Numbers – Applying properties of numbers, particularly how to find a missing number when one number and its HCF and LCM with another number are known.