# CAT Practice : Number System - HCF, LCM

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When a number is divided by 8, a remainder of 7 can be thought of as a remainder of -1. This idea is very useful in a bunch of questions.

## Number Theory - Remainders LCM

Q.2: Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?
1. 2519
2. 5039
3. 1079
4. 979

Choice A. 2519

## Detailed Solution

LCM (5, 6, 7, 8, 9) - 1 = 2519.
Choice (A)

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## More questions from Number Theory - HCF, LCM

Number Theory is one of the most heavily tested topics. Within this, one should get the basics on factors, multiples, HCF, LCM very clear before moving on to the tougher sets.