If the LCM of two numbers is 72 and one of the numbers is 8, what is the other n

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Question: If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?

Options:

Correct Answer: 18

Solution:

The other number can be found using the formula LCM(a, b) = (a * b) / HCF(a, b). Here, 72 = (8 * x) / HCF(8, x). The other number is 18.

If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?

If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?

Correct Answer: 18

Step 1: Understand that LCM stands for Least Common Multiple, which is the smallest number that is a multiple of both numbers.
Step 2: We know one number is 8 and the LCM of the two numbers is 72.
Step 3: Use the formula for LCM: LCM(a, b) = (a * b) / HCF(a, b), where HCF is the Highest Common Factor.
Step 4: Substitute the known values into the formula: 72 = (8 * x) / HCF(8, x).
Step 5: Rearrange the formula to find x: 72 * HCF(8, x) = 8 * x.
Step 6: To find HCF(8, x), we need to consider the factors of 8 and x. The HCF will be a factor of both numbers.
Step 7: Since we want to find x, we can try different values for x that would make the equation true.
Step 8: After testing values, we find that when x = 18, the equation holds true.
Step 9: Therefore, the other number is 18.

Least Common Multiple (LCM) – The LCM of two numbers is the smallest multiple that is evenly divisible by both numbers.
Highest Common Factor (HCF) – The HCF of two numbers is the largest number that divides both of them without leaving a remainder.
Relationship between LCM and HCF – The relationship between LCM and HCF can be expressed as LCM(a, b) = (a * b) / HCF(a, b).