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

SAMARPITA DUTTA 1 year 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 2 years ago
very helpful.........thanks :)

Anbu Sudha 2 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 
poonam rajpal 3 years ago
SIR,THIS MUCH OF PREPARTION IS ENOUGH FOR PASSING THE ENTRANCE....

Sravya 3 years ago
Some answers are not correct.

nadeem 3 years ago
very helpful wbsite i love it

Alok Singh 3 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. 
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

no one 4 years ago
you have not my answer

Swati 4 years ago
Thanx for your great questions...It helps me a lot in my preparation

Sahil Arora 4 years ago
Thanks mastguru.. keep it up.

Shikha 4 years ago
Thanks for awesome questions answers collection..
Love you guys.... Sooooooo helpful