If the HCF of two numbers is 8 and their product is 288, what is their LCM? (202

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Question: If the HCF of two numbers is 8 and their product is 288, what is their LCM? (2023)

Options:

Correct Answer: 36

Exam Year: 2023

Solution:

Using the relationship between HCF, LCM, and the product of two numbers: LCM = Product / HCF = 288 / 8 = 36.

If the HCF of two numbers is 8 and their product is 288, what is their LCM? (2023)

If the HCF of two numbers is 8 and their product is 288, what is their LCM? (2023)

Step 1: Understand the terms. HCF (Highest Common Factor) is the largest number that divides both numbers. LCM (Lowest Common Multiple) is the smallest number that both numbers can divide into.
Step 2: Note the given values. The HCF of the two numbers is 8, and their product is 288.
Step 3: Use the relationship between HCF, LCM, and the product of the two numbers. The formula is: LCM = (Product of the two numbers) / (HCF).
Step 4: Substitute the known values into the formula. LCM = 288 / 8.
Step 5: Perform the division. 288 divided by 8 equals 36.
Step 6: Conclude that the LCM of the two numbers is 36.

HCF and LCM Relationship – The relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers is given by the formula: LCM = (Product of the two numbers) / HCF.