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} 128
 126
 146
 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
 18
 36
 54
 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. \begin{aligned} \frac{30}{25} \end{aligned}
 \begin{aligned} \frac{28}{29} \end{aligned}
 \begin{aligned} \frac{28}{29} \end{aligned}
 \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. \begin{aligned} \frac{11}{12} \end{aligned}
 \begin{aligned} \frac{23}{24} \end{aligned}
 \begin{aligned} \frac{26}{27} \end{aligned}
 \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 \begin{aligned} 2^4 \times 3^4 \times 5^3 \end{aligned}
 \begin{aligned} 2^4 \times 3^4 \times 5^3 \times 11 \end{aligned}
 \begin{aligned} 2^2 \times 3^2 \times 5^2 \end{aligned}
 \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
 54
 108
 216
 432
Answer And Explanation
Answer: Option C
Explanation:
LCM of 8243654 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}
 \begin{aligned} \frac{2}{27} \end{aligned}
 \begin{aligned} \frac{8}{3} \end{aligned}
 \begin{aligned} \frac{2}{3} \end{aligned}
 \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