PYQ Vault
EbooksTutor

Largest or smallest number with given remainder r for several divisors: k x LCM + r

This type of question, asked 5 times: CDS 2 2018, CDS 1 2023, CDS 2 2024, CDS 1 2025, CDS 2 2025. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2018

    1
    The highest four-digit number which is divisible by each of the numbers 16, 36, 45, 48 is

    Tap an option to check your answer.

  2. Question 2

    CDS 1 2023

    18
    What is the largest 5-digit number, which leaves remainder 7, when divided by 18 as well as by 11?

    Tap an option to check your answer.

  3. Question 3

    CDS 2 2024

    7
    Let NN be the least positive multiple of 11 that leaves a remainder of 5 when divided by 6, 12, 15, 18. Which one of the following is correct ?

    Tap an option to check your answer.

  4. Question 4

    CDS 1 2025

    6
    N is the smallest 5-digit number which when divided by 2,22,23,24,…,2n2, 2^2, 2^3, 2^4, \ldots, 2^n leaves a remainder 1. What is the value of nn ?

    Tap an option to check your answer.

  5. Question 5

    CDS 2 2025

    30
    A number NN is such that when divided by 4, 6, 7 or 9, it leaves 3 as remainder. What is the smallest 4-digit number that satisfies this property?

    Tap an option to check your answer.