What is the smallest number greater than (1000) that is exactly divisible by (36), (48), and (60)?
Answer and explanation
Correct answer: (1440)
Step 1: First find the LCM of (36), (48), and (60). Step 2: (36=2^2\times 3^2), (48=2^4\times 3), (60=2^2\times 3\times 5), so the LCM is (2^4\times 3^2\times 5=720). The smallest multiple greater than (1000) is (1440). Step 3: Find the LCM first, then choose its multiple according to the limit.
Frequently asked questions
What is the correct answer to this question?
(1440)
Why is this the correct answer?
Step 1: First find the LCM of (36), (48), and (60). Step 2: (36=2^2\times 3^2), (48=2^4\times 3), (60=2^2\times 3\times 5), so the LCM is (2^4\times 3^2\times 5=720). The smallest multiple greater than (1000) is (1440). Step 3: Find the LCM first, then choose its multiple according to the limit.
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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