HCF and LCM Questions Answers

  • 1. Find the HCF of
    \begin{aligned}
    2^2 \times 3^2 \times 7^2, 2 \times 3^4 \times 7
    \end{aligned}

    1. 128
    2. 126
    3. 146
    4. 434
    Answer And Explanation

    Answer: Option B

    Explanation:

    HCF is Highest common factor, so we need to get the common highest factors among given values. So we got
    2 * 3*3 * 7

  • 2. Find the HCF of 54, 288, 360

    1. 18
    2. 36
    3. 54
    4. 108
    Answer And Explanation

    Answer: Option A

    Explanation:

    Lets solve this question by factorization method.

    \begin{aligned}
    18 = 2 \times 3^2, 288 = 2^5 \times 3^2, 360 = 2^3 \times 3^2 \times 5
    \end{aligned}

    So HCF will be minimum term present in all three, i.e.
    \begin{aligned}
    2 \times 3^2 = 18
    \end{aligned}

  • 3. Reduce \begin{aligned}
    \frac{368}{575}
    \end{aligned} to the lowest terms.

    1. \begin{aligned} \frac{30}{25} \end{aligned}
    2. \begin{aligned} \frac{28}{29} \end{aligned}
    3. \begin{aligned} \frac{28}{29} \end{aligned}
    4. \begin{aligned} \frac{16}{25} \end{aligned}
    Answer And Explanation

    Answer: Option D

    Explanation:

    We can do it easily by in two steps
    Step1: We get the HCF of 368 and 575 which is 23
    Step2: Divide both by 23, we will get the answer 16/25

  • 4. Reduce \begin{aligned}
    \frac{803}{876}
    \end{aligned} to the lowest terms.

    1. \begin{aligned} \frac{11}{12} \end{aligned}
    2. \begin{aligned} \frac{23}{24} \end{aligned}
    3. \begin{aligned} \frac{26}{27} \end{aligned}
    4. \begin{aligned} \frac{4}{7} \end{aligned}
    Answer And Explanation

    Answer: Option A

    Explanation:

    HCF of 803 and 876 is 73, Divide both by 73, We get the answer 11/12

  • 5. HCF of
    \begin{aligned}
    2^2 \times 3^2 \times 5^2, 2^4 \times 3^4 \times 5^3 \times 11
    \end{aligned} is

    1. \begin{aligned} 2^4 \times 3^4 \times 5^3 \end{aligned}
    2. \begin{aligned} 2^4 \times 3^4 \times 5^3 \times 11 \end{aligned}
    3. \begin{aligned} 2^2 \times 3^2 \times 5^2 \end{aligned}
    4. \begin{aligned} 2 \times 3 \times 5 \end{aligned}
    Answer And Explanation

    Answer: Option C

    Explanation:

    As in HCF we will choose the minimum common factors among the given.. So answer will be third option

  • 6. What will be the LCM of 8, 24, 36 and 54

    1. 54
    2. 108
    3. 216
    4. 432
    Answer And Explanation

    Answer: Option C

    Explanation:

    LCM of 8-24-36-54 will be
    2*2*2*3*3*3 = 216

  • 7. Find the HCF of \begin{aligned} \frac{2}{3}, \frac{4}{6}, \frac{8}{27} \end{aligned}

    1. \begin{aligned} \frac{2}{27} \end{aligned}
    2. \begin{aligned} \frac{8}{3} \end{aligned}
    3. \begin{aligned} \frac{2}{3} \end{aligned}
    4. \begin{aligned} \frac{8}{27} \end{aligned}
    Answer And Explanation

    Answer: Option A

    Explanation:

    Whenever we have to solve this sort of question, remember the formula.
    HCF = \begin{aligned} \frac{HCF of Numerators}{LCM of Denominators} \end{aligned}
    So answers will be option 1

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