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Rainbow [258]
3 years ago
5

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the two numbers.

Mathematics
1 answer:
Naddik [55]3 years ago
5 0
Sol. (1) Prime factors of 26 = 2 x 13
Prime factors of 91 = 7 x 13
Hence, HCF = Common factors between 26 and 91 =13 and LCM=13x2x7=182

Now product of numbers 26 and 91
= 26 x 91 = 2366 and Product of HCF and LCM = 13 x 182 = 2366

So, it verify that product of two numbers = Product of HCF and LCM.

(2) Prime factors of 510 = 2 x 3 x 5 x 17
Prime factors of 92 = 2 x 2 x 23
Hence,HCF=2 and LCM=2×2×3 × 5×17×23 =23460

Now product of Numbers 510 and 92 = 46920 and product of HCF and LCM = 2 x 23460= 46920

Hence, verified that product of two numbers 18 equal to product of their HCF and LCM.

(3) Prime factors of336 = 2 x 2 x 2 x 2 x 3 x 7

Prime factors of 54 = 2 x 3 x 3 x 3
Hence, HCF (Product of common factors of 336 and 54)
=2 x 3=6

And LCM (Product of all common factors with remaining factors)
=(2 x 3)x 2 x 2 x 2 x 3 x 3 x 7=3024

Now, product of numbers 336 and 54 = 336 x 54 = 18144
and product of HCF and LCM = 6 x 3024 = 18144
Hence, product of two numbers: Product of HCF and LCM.
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in a square garden plot (with an area of 400 sq ft)deer fencing priced at $1.50 per foot is to be installed around the plot. if
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We have a square garden of 400 square foot.

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In this case:

\begin{gathered} A=400=x^2 \\ x=\sqrt[]{400}=20\text{ ft} \end{gathered}

The perimeter of the square is the sum of the lengths of the sides of the square. As they are all equal, we can write:

P=4x=4\cdot20=80\text{ ft}

The fencing is priced at $1.50 per foot. If we add the 7% sales tax to this price we get:

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The fencing will be installed in all the perimeter (80 ft).

We can calculate the total cost by multiplying the sales price ($1.605 per foot) and the perimeter (80 ft):

F=C\cdot P=1.605\frac{\text{\$}}{\text{ft}}\cdot80\text{ ft}=\$128.40

Answer: the fencing will cost a total of $128.40

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