The LCM of two numbers is 84 and their HCF is 12. If one of the numbers is 36, w

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Question: The LCM of two numbers is 84 and their HCF is 12. If one of the numbers is 36, what is the other number? (2023)

Options:

Correct Answer: 28

Exam Year: 2023

Solution:

Using the relation: LCM * HCF = Product of the numbers, we have 84 * 12 = 36 * x, solving gives x = 28.

The LCM of two numbers is 84 and their HCF is 12. If one of the numbers is 36, what is the other number? (2023)

The LCM of two numbers is 84 and their HCF is 12. If one of the numbers is 36, what is the other number? (2023)

Step 1: Understand the relationship between LCM, HCF, and the two numbers. The formula is: LCM * HCF = Number 1 * Number 2.
Step 2: Identify the values given in the question. LCM = 84, HCF = 12, and one of the numbers (Number 1) = 36.
Step 3: Substitute the known values into the formula: 84 * 12 = 36 * Number 2.
Step 4: Calculate the left side of the equation: 84 * 12 = 1008.
Step 5: Now, the equation looks like this: 1008 = 36 * Number 2.
Step 6: To find Number 2, divide both sides of the equation by 36: Number 2 = 1008 / 36.
Step 7: Perform the division: 1008 ÷ 36 = 28.
Step 8: Therefore, the other number is 28.

LCM and HCF Relationship – The relationship between the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers, which states that the product of the LCM and HCF equals the product of the two numbers.