Question:
The LCM of two numbers is 15 times their HCF. If the sum of their LCM and HCF is 160 and one of the numbers is 50, then what is the other number?
The LCM of two numbers is 15 times their HCF. If the sum of their LCM and HCF is 160 and one of the numbers is 50, then what is the other number?
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Product of two numbers = LCM × HCF
Updated On: Apr 21, 2026
- 20
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The Correct Option is C
Solution and Explanation
Step 1: Define HCF and LCM.
Let HCF = \(h\), LCM = \(15h\). Step 2: Use given sum.
\(h + 15h = 160\).
\(16h = 160\).
\(h = 10\).
Then LCM = \(15 \times 10 = 150\). Step 3: Use product formula.
For two numbers \(a\) and \(b\): \(a \times b = \text{LCM} \times \text{HCF}\).
\(50 \times b = 150 \times 10 = 1500\).
\(b = \frac{1500}{50} = 30\).
Let HCF = \(h\), LCM = \(15h\). Step 2: Use given sum.
\(h + 15h = 160\).
\(16h = 160\).
\(h = 10\).
Then LCM = \(15 \times 10 = 150\). Step 3: Use product formula.
For two numbers \(a\) and \(b\): \(a \times b = \text{LCM} \times \text{HCF}\).
\(50 \times b = 150 \times 10 = 1500\).
\(b = \frac{1500}{50} = 30\).
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