If the HCF of 18 and 24 is 6, what is the LCM of these two numbers? (2023)

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Question: If the HCF of 18 and 24 is 6, what is the LCM of these two numbers? (2023)

Options:

Correct Answer: 72

Exam Year: 2023

Solution:

Using the relation HCF * LCM = Product of the numbers, we have 6 * LCM = 18 * 24. Thus, LCM = (18 * 24) / 6 = 72.

If the HCF of 18 and 24 is 6, what is the LCM of these two numbers? (2023)

If the HCF of 18 and 24 is 6, what is the LCM of these two numbers? (2023)

Step 1: Identify the two numbers we are working with, which are 18 and 24.
Step 2: Recall the relationship between HCF (Highest Common Factor) and LCM (Lowest Common Multiple), which is: HCF * LCM = Product of the two numbers.
Step 3: We know the HCF of 18 and 24 is 6.
Step 4: Calculate the product of the two numbers: 18 * 24.
Step 5: Perform the multiplication: 18 * 24 = 432.
Step 6: Now, use the relationship: 6 * LCM = 432.
Step 7: To find LCM, divide both sides of the equation by 6: LCM = 432 / 6.
Step 8: Perform the division: 432 / 6 = 72.
Step 9: Therefore, the LCM of 18 and 24 is 72.

HCF and LCM Relationship – Understanding the relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers, specifically that HCF * LCM = Product of the numbers.