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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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<img src="https://tex.z-dn.net/?f=%5Ctext%7BSolve%20for%20x%3A%7D%5C%5C%5C%5C3x%20%2B%2065%20%3D%20523%5C%5C%5C%5C%5Ctext%7BThan
Vlad1618 [11]

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

{x=152.666....

»»————- ★ ————-««  

Here’s why:

⸻⸻⸻⸻

\boxed{\text{Solving for x...}}\\\\3x+ 65= 523\\----------\\\rightarrow 3x + 65 - 65=523-65\\\\\rightarrow 3x = 458\\\\\rightarrow\frac{3x = 458}{3}\\\\\rightarrow  \boxed{x=152.666....}

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

7 0
2 years ago
Read 2 more answers
GIVING BRAINLIEST FOR WHO ANSWERS FIRST!
Fantom [35]

Answer:

its simple its C

Step-by-step explanation:

forget humanity and return to monke

3 0
3 years ago
Read 2 more answers
Melissa, Dan, and Henry have $87 in their wallets. Dan has 3 times what Henry has. Melissa has $8 less than Henry. How much does
puteri [66]

Answer:

Henry has $19, Dan has $57, and Melissa has $11

Step-by-step explanation:

Let x represent how much money Henry has

Since Dan has 3 times what Henry has, his amount is 3x

Since Melissa has $8 less than Henry, her amount is x - 8

Create an equation that sets these 3 values equal to 87, then solve for x

(x) + (3x) + (x - 8) = 87

5x - 8 = 87

5x = 95

x = 19

So, Henry has $19

Find how much Dan has by multiplying 19 by 3

19(3)

= 57

Find how much Melissa has by subtracting 8 from 19

19 - 8

= 11

So, Henry has $19, Dan has $57, and Melissa has $11

8 0
2 years ago
Read 2 more answers
if you have four rolls of quarters three rolls of Dimes and six rolls of nickels how much do you have
xz_007 [3.2K]
We know that
the number of coins that each roll contains is
<span>rolls of quarters-------> 40 coins
</span><span>rolls of Dimes---------> 50 coins
</span><span>rolls of nickels------> 40 coins

</span><span>four rolls of quarters------> 4*40*$0.25-----> $40
</span>t<span>hree rolls of Dimes-----> 3*50*$0.10------> $15
</span><span>six rolls of nickels-------> 6*40*$0.05-----> $12

total=[40+15+12]------> $67

the answer is
$67</span>
3 0
3 years ago
I need a y=mx+b problem
Anna35 [415]

Answer: y=x^2

Step-by-step explanation: There are first of all squares, so you have to multiply the sides. Well and the figure 2 has a side of two smaller squares. So you know x is the argument, in this case the number of the figure, because it is regularly you know that x as example for figure 7 is seven so you have to multiply 7 by 7. This isn’t linear.

5 0
3 years ago
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