A number leaves remainders (38), (68), and (83) when divided by (45), (75), and (90) respectively. What is the smallest such number?
Answer and explanation
Correct answer: (443)
Step 1: In each case, divisor minus remainder is (7), so adding (7) to the number makes it divisible by all three divisors. Step 2: The LCM of (45), (75), and (90) is (450), so the number is (450-7=443). Step 3: Spot the common difference and subtract it from the LCM.
Frequently asked questions
What is the correct answer to this question?
(443)
Why is this the correct answer?
Step 1: In each case, divisor minus remainder is (7), so adding (7) to the number makes it divisible by all three divisors. Step 2: The LCM of (45), (75), and (90) is (450), so the number is (450-7=443). Step 3: Spot the common difference and subtract it from the LCM.
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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