# 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

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

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}

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}

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}

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

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}

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