If the LCM of three numbers is 180 and their HCF is 3, what is the product of th

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

Options:

Correct Answer: 5400

Exam Year: 2023

Solution:

The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.

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

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

Step 1: Understand that LCM stands for Least Common Multiple and HCF stands for Highest Common Factor.
Step 2: Note the values given in the question: LCM = 180 and HCF = 3.
Step 3: Recall the formula that relates the product of the numbers to their LCM and HCF: Product of the numbers = LCM * (HCF^2).
Step 4: Calculate HCF squared: 3^2 = 9.
Step 5: Multiply the LCM by HCF squared: 180 * 9.
Step 6: Perform the multiplication: 180 * 9 = 1620.
Step 7: Conclude that the 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 numbers equals the LCM multiplied by the HCF raised to the power of the number of elements minus one.