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If the LCM of two numbers is 120 and one of the numbers is 30, what is the other
If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?
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Q1
If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?
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The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.
Questions & Step-by-step Solutions
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Q
Q: If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?
Solution:
The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.
Steps: 10
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 the LCM of the two numbers is 120.
Step 3: One of the numbers is given as 30.
Step 4: We need to find the other number, which we will call 'b'.
Step 5: Use the formula for LCM: LCM = (a * b) / HCF, where 'a' is 30 and 'b' is the unknown number.
Step 6: We can rearrange the formula to find 'b': b = (LCM * HCF) / a.
Step 7: We need to assume the Highest Common Factor (HCF) of 30 and 'b'. A common assumption is that HCF is 30.
Step 8: Substitute the values into the formula: b = (120 * 30) / 30.
Step 9: Simplify the equation: b = 120.
Step 10: Since we assumed HCF is 30, we can also check if HCF is actually 30. If it is, then b = 40 is correct.
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