# 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

• #### SAMARPITA DUTTA 5 years ago

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

• #### Sumit 5 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

• #### Anbu Sudha 6 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 6 years ago replied

welcome Tanima !

#### Arun 5 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 4 years ago replied

Same query, I think it is a mistake.

#### mastguru 6 years ago replied

thank you Taha !

• #### poonam rajpal 6 years ago

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

• #### nadeem 7 years ago

very helpful wbsite i love it

• #### Jayesh 7 years ago

Awesome website for competitive exam preparation
Thank you sir

#### mastguru 7 years ago replied

Thank you Jayesh for your feedback..

• #### Alok Singh 7 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.

tnx sir....

#### mastguru 7 years ago replied

Most welcome :)

• #### Ruchi Malik Sharma 7 years ago

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

• #### Ruchi Malik Sharma 7 years ago

Q12 : havin wrong Ans

HCF of : 1575,1125,765

45 Ans

• #### Sri 7 years ago

very very useful

• #### Swati 7 years ago

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

• #### neetu 8 years ago

thanx mastguru....

#### Ashish rajput 6 years ago replied

thanku mastguru side..

• #### Sahil Arora 8 years ago

Thanks mastguru.. keep it up.

• #### Shikha 8 years ago

Thanks for awesome questions answers collection..