The HCF of two numbers is 7 and their LCM is 84. If one of the numbers is 21, wh

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Question: The HCF of two numbers is 7 and their LCM is 84. If one of the numbers is 21, what is the other number? (2023)

Options:

Correct Answer: 42

Exam Year: 2023

Solution:

Using the relation HCF * LCM = Product of the numbers, we have 7 * 84 = 21 * x, which gives x = 42.

The HCF of two numbers is 7 and their LCM is 84. If one of the numbers is 21, what is the other number? (2023)

The HCF of two numbers is 7 and their LCM is 84. If one of the numbers is 21, what is the other number? (2023)

Step 1: Understand the problem. We need to find the other number when we know the HCF (7), LCM (84), and one number (21).
Step 2: Recall the relationship between HCF, LCM, and the two numbers. The formula is: HCF * LCM = Number1 * Number2.
Step 3: Substitute the known values into the formula. We have: 7 * 84 = 21 * x, where x is the other number.
Step 4: Calculate the left side of the equation. 7 * 84 = 588.
Step 5: Now we have the equation: 588 = 21 * x.
Step 6: To find x, divide both sides of the equation by 21. So, x = 588 / 21.
Step 7: Calculate 588 divided by 21. This gives us x = 28.
Step 8: Therefore, the other number is 28.

HCF and LCM Relationship – The relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers, which states that the product of the HCF and LCM equals the product of the two numbers.
Finding Unknowns – Using known values to find an unknown number in a mathematical relationship.