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What is the smallest number that leaves remainders of 1, 2, 3, 4, and 5 when divided by 6, 7, 8, 9, and 10 respectively, and is also exactly divisible by 19?

Problems on L.C.M and H.C.F MCQs for PPSC, FPSC, NTS, and Pakistan government job tests. Select an option below, then read the explanation.

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Problems on L.C.M and H.C.Fmathematics-mcqs › problems-on-l-c-m-and-h-c-f
Published
12 Jul 2019
Last updated
28 May 2026

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Explanation

The number must satisfy the conditions of leaving specific remainders when divided by 6, 7, 8, 9, and 10, and be divisible by 19 without remainder. Among the given choices, only 5035 meets all these criteria.

More Problems on L.C.M and H.C.F MCQs

Practice related questions from the same subject.

  1. 1.What is the smallest perfect square that is divisible by 10, 12, 15, and 18?
  2. 2.Three men begin simultaneously to run along a circular track that measures 11 kilometers in circumference. Their speeds are 4 km/h, 5 km/h, and 8 km/h respectively. After how many hours will they all meet again at the starting point together?
  3. 3.What is the smallest multiple of 13 that, when divided by 6, 8, and 12, leaves remainders of 5, 7, and 11 respectively?
  4. 4.What is the smallest number that leaves remainders of 1, 2, 3, 4, and 5 when divided by 2, 3, 4, 5, and 6 respectively, and is exactly divisible by 7?
  5. 5.A pile of stones can be evenly divided into groups of 21 without any remainder. However, when the stones are grouped into sets of 16, 20, 25, or 45, there are always 3 stones left over. What is the smallest possible number of stones in the pile?
  6. 6.What is the largest four-digit number that leaves remainders of 4, 9, 15, and 22 when divided by 10, 15, 21, and 28 respectively?
  7. 7.What is the smallest number that leaves a remainder of 25 when divided by 35, a remainder of 15 when divided by 25, and a remainder of 5 when divided by 15?
  8. 8.Find the smallest number that, when divided by 8, 12, 18, and 24, leaves remainders of 4, 8, 14, and 20 respectively.
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