If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possi
Practice Questions
Q1
If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)
540
1800
5400
18000
Questions & Step-by-Step Solutions
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.
