If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possi

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Question: If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)

Options:

Correct Answer: 5400

Exam Year: 2023

Solution:

The maximum product of the three numbers can be calculated as (LCM * HCF^2) = 180 * 3^2 = 5400.

If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)

If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)

Step 1: Understand the terms LCM and HCF. LCM (Least Common Multiple) is the smallest number that is a multiple of all the numbers. HCF (Highest Common Factor) is the largest number that divides all the numbers.
Step 2: Identify the values given in the question. The LCM of the three numbers is 180, and the HCF is 3.
Step 3: Use the formula for the product of the numbers in terms of LCM and HCF. The formula is: Product of the numbers = LCM * HCF^2.
Step 4: Substitute the values into the formula. Here, LCM = 180 and HCF = 3.
Step 5: Calculate HCF squared. HCF^2 = 3^2 = 9.
Step 6: Now multiply LCM by HCF squared. So, 180 * 9 = 1620.
Step 7: The maximum possible product of the three numbers is 1620.

LCM and HCF Relationship – The relationship between the least common multiple (LCM) and the highest common factor (HCF) of a set of numbers, specifically that the product of the LCM and HCF of a set of numbers equals the product of the numbers themselves.
Maximizing Product – Understanding how to maximize the product of numbers given their LCM and HCF by manipulating their values while adhering to the constraints provided.