Question Detail

Find the LCM 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: Option B

Explanation:

Whenever we have to solve this sort of question, remember the formula.
LCM = \\begin{aligned} \\frac{HCF of Denominators}{LCM of Numerators} \\end{aligned}
So answers will be option 2,
Please also give attention to the difference in formula of HCF and LCM

1. Find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively

Answer: Option B

Explanation:

In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1661 - 10) and (2045 -13)
= HCF (1651, 2032) = 127

2. If the product of two numbers is 84942 and their H.C.F. is 33, find their L.C.M.

2574
2500
1365
1574

Answer: Option A

Explanation:

HCF * LCM = 84942, because we know

Product of two numbers = Product of HCF and LCM

LCM = 84942/33 = 2574

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: 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: Option A

Explanation:

HCF of 803 and 876 is 73, Divide both by 73, We get the answer 11/12

5. Find the HCF of 54, 288, 360

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}