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If the LCM of two numbers is 72 and one of the numbers is 8, what is the other n
If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?
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Practice Questions
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Q1
If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?
9
18
36
72
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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.
Questions & Step-by-step Solutions
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Q
Q: If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?
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.
Steps: 9
Show Steps
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.
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