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

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• 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.
  $$\begin{aligned} 2 \times 3^2 = 18 \end{aligned}$$
  

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• 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

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• 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

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• 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

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• 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

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• 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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