If the LCM of two numbers is 72 and one of the numbers is 24, what is the other

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Question: If the LCM of two numbers is 72 and one of the numbers is 24, what is the other number? (2023)

Options:

Correct Answer: 36

Exam Year: 2023

Solution:

Using the relationship between LCM and the numbers: (24 * x) / HCF = 72. The other number is 36.

If the LCM of two numbers is 72 and one of the numbers is 24, what is the other number? (2023)

If the LCM of two numbers is 72 and one of the numbers is 24, what is the other number? (2023)

Step 1: Understand that LCM stands for Least Common Multiple.
Step 2: We know the LCM of two numbers is 72.
Step 3: One of the numbers is given as 24.
Step 4: Let the other number be 'x'.
Step 5: Use the formula: LCM = (Number1 * Number2) / HCF.
Step 6: Rearrange the formula to find 'x': LCM * HCF = Number1 * Number2.
Step 7: Substitute the known values into the formula: 72 * HCF = 24 * x.
Step 8: To find 'x', we need to know the HCF (Highest Common Factor) of 24 and 'x'.
Step 9: Since we are looking for 'x' that gives LCM of 72, we can try different values.
Step 10: If we try 'x' = 36, we check: LCM(24, 36) = 72.
Step 11: Since it works, we conclude that the other number is 36.

LCM and HCF Relationship – The relationship between the Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two numbers is given by the formula: LCM(a, b) = (a * b) / HCF(a, b).
Finding the Other Number – To find the other number when one number and the LCM are known, rearranging the LCM formula can help derive the unknown value.