LCM with Remainders
Concepts Examples

There are three types of questions that are based on LCM with remainders. They are as follows.

  1. When the remainders are same for all the divisors

    In this case the required number will be the LCM × N + remainder, where N is any natural number

    N=1, will give smallest such number

    N=2, will give second smallest such number and so on

  2. When the remainders are different for different divisors but the respective difference between the divisors and the remainders remain constant.

    In this case the required number will be LCM × N +difference of any (divisor - remainder)

    refer to example 2.

  3. When neither the divisors are same nor the respective difference between the divisors and the remaniders remain constant.

    In this case solve the question by forming equations and solving them.

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