If the LCM of two numbers is 60 and one of the numbers is 15, what is the other

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Question: If the LCM of two numbers is 60 and one of the numbers is 15, what is the other number?

Options:

Correct Answer: 30

Solution:

Using the relation LCM(a, b) = (a * b) / HCF(a, b), we can find the other number. Here, 60 = (15 * x) / HCF(15, x). The other number is 60 / 15 = 4.

If the LCM of two numbers is 60 and one of the numbers is 15, what is the other number?

If the LCM of two numbers is 60 and one of the numbers is 15, what is the other number?

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 the LCM of the two numbers is 60.
Step 3: One of the numbers is given as 15.
Step 4: We need to find the other number, which we will call 'x'.
Step 5: Use the formula for LCM: LCM(a, b) = (a * b) / HCF(a, b). Here, a is 15 and b is x.
Step 6: Rewrite the formula with the known values: 60 = (15 * x) / HCF(15, x).
Step 7: To find x, we can rearrange the equation. First, multiply both sides by HCF(15, x): 60 * HCF(15, x) = 15 * x.
Step 8: Now, we can also use the fact that LCM(15, x) = 60 to find a relationship between 15 and x.
Step 9: Since 60 is the LCM, we can also say that 60 = 15 * (x / HCF(15, x)).
Step 10: To find x, we can simplify: x = (60 * HCF(15, x)) / 15.
Step 11: Since HCF(15, x) must be a factor of 15, we can try different factors of 15 (1, 3, 5, 15) to find x.
Step 12: If we try HCF(15, x) = 15, we get x = (60 * 15) / 15 = 60, which is not valid since LCM must be 60.
Step 13: If we try HCF(15, x) = 3, we get x = (60 * 3) / 15 = 12.
Step 14: Check if LCM(15, 12) = 60. Yes, it is correct.
Step 15: Therefore, the other number is 12.

Least Common Multiple (LCM) – Understanding the relationship between LCM, HCF (Highest Common Factor), and the two numbers involved.
Basic Arithmetic Operations – Applying multiplication and division to solve for the unknown number.