A number leaves remainders (43), (67), and (115) when divided by (48), (72), and (120) respectively. What is the smallest such number?
Answer and explanation
Correct answer: (715)
Step 1: In each case, the difference between divisor and remainder is (5), so adding (5) to the number makes it divisible by (48), (72), and (120). Step 2: Their LCM is (720), so the smallest number is (720-5=715). Step 3: In such questions, spotting the common difference makes the calculation much easier.
Frequently asked questions
What is the correct answer to this question?
(715)
Why is this the correct answer?
Step 1: In each case, the difference between divisor and remainder is (5), so adding (5) to the number makes it divisible by (48), (72), and (120). Step 2: Their LCM is (720), so the smallest number is (720-5=715). Step 3: In such questions, spotting the common difference makes the calculation much easier.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: HCF and LCM using prime factorisation.
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