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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

Post a comment

  • SAMARPITA DUTTA 2 years ago

    HOW LCM COMES 27 WHERE 3 NUMBERS ARE 3,6 AND 27 ?? PLEASE EXPLAIN THIS...

  • Sumit 2 years ago

    Why nobody notice it. In the 7th question the lcm of denominator is 54 and not 27. 27 is not a multiple of 6

  • Tanima Guha 3 years ago

    very helpful.........thanks :-)

  • Anbu Sudha 3 years ago

    Very useful sir.
    But one doubt LCM IS 24. ONE NUMBER IS 8 WHAT IS HCF AND OTHER NUMBER PLEASE TELL WITH FULL STEP ANSWER

    mastguru 3 years ago replied

    welcome Tanima !

    Arun 2 years ago replied

    Indeed the LCM would be 54 and so the answer would be 1/27 and not 2/27

    i-love-samarpita-dutta 1 year ago replied

    Same query, I think it is a mistake.

  • Taha Muhammad 3 years ago

    very helpful

    mastguru 3 years ago replied

    thank you Taha !

  • poonam rajpal 3 years ago

    SIR,THIS MUCH OF PREPARTION IS ENOUGH FOR PASSING THE ENTRANCE....

  • Sravya 4 years ago

    Some answers are not correct.

  • nadeem 4 years ago

    very helpful wbsite i love it

  • Jayesh 4 years ago

    Awesome website for competitive exam preparation
    Thank you sir

    mastguru 4 years ago replied

    Thank you Jayesh for your feedback..

  • Alok Singh 4 years ago

    In Q.7 , all the given options are wrong. the right answer is 1/27.

    Because the H.C.F of 2,4 and 8 is 2
    and L.C.M of 3,6 and 27 is 54
    so it will be 2/54 = 1/27.

  • Mohd Asif 4 years ago

    tnx sir....

    mastguru 4 years ago replied

    Most welcome :)

  • Ruchi Malik Sharma 4 years ago

    solution of the que no 16 not appropriate please provide us right solution of the que no 16

  • Ruchi Malik Sharma 4 years ago

    Q12 : havin wrong Ans

    HCF of : 1575,1125,765

    45 Ans

  • Charu Jain 4 years ago

    quite helpful!!

    mastguru 4 years ago replied

    Thanks Charu for your feedback.

  • Sri 4 years ago

    very very useful

    mastguru 4 years ago replied

    Thanks Sri for your feedback.

  • no one 5 years ago

    you have not my answer

  • Swati 5 years ago

    Thanx for your great questions...It helps me a lot in my preparation

  • neetu 5 years ago

    thanx mastguru....

    Ashish rajput 4 years ago replied

    thanku mastguru side..

  • Sahil Arora 5 years ago

    Thanks mastguru.. keep it up.

  • Shikha 5 years ago

    Thanks for awesome questions answers collection..
    Love you guys.... Sooooooo helpful