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UPSC Prelims

Mathematics

Theme:

LCM AND HCF / लघुत्तम समापवर्त्य एवं महत्तम समापवर्तक

Q65 2022, LCM AND HCF

What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?

1000 से बड़ी वह लघुतम संख्या कौन-सी है जिसे 6, 9, 12, 15, 18 में से किसी एक से भी विभाजित करें, तो शेषफल 3 बचे?

Explanation Please wait..

LCM of 6, 9, 12, 15, 18 = 180.

Means this is the smallest number that will be divided by every number.

Such number above 1000 will also be a multiplication of 180.

180 × 5 = 900 < 1000

180 × 6 = 1080. > 1000 however this is the smallest multiple of 180 above 1000.

Now, we need the remainder as 3. So, desired number = 1083.

This question can also be solved backward by trying every options.

व्याख्या Please wait..

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