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)

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Q: 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)

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

Steps: 8

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.