All categories

3 years ago

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

1 answer:

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.

You might be interested in

We found the correlation coefficient for the comparison between height and weight in babies to be -0.12. That meanscorrelation i

qwelly [4]

Answer:

The taller the baby, the lighter the baby

Explanation:

A correlation coefficient is a number between -1 and 1. The correlation is strong when it is a number closer to -1 or closer to 1 and the relation is independent when it is a number closer to 0.

In this case, we get that the correlation coefficient is -0.12, so there is a weak negative correlation. The negative means that when one variable increases, the other decrease, so the taller the baby, the lighter the baby.

Then, the answer is:

The taller the baby, the lighter the baby

6 0

1 year ago

Find the sum of the squares of the roots of 3x^2 + 4x + 12 = 0

Contact [7]

Answer:

-56/9

Step-by-step explanation:

Let p and q be the roots of the equation.

So, here's how we're gonna work it out:

${p}^{2} + {q}^{2} = \\ {p}^{2} + {q}^{2} +2 pq - 2pq = \\ ( {p}^{2} +2pq + {q}^{2}) - 2pq = \\ {(p + q)}^{2} - 2pq$

Vieta's formulas give us the sum and the product of the roots of a quadratic equation. Using them we obtain:

p + q = -b / a = - 4 / 3
p × q = c / a = 12 / 3 = 4

${(p + q)}^{2} - 2pq = \\ {( - \frac{ 4}{3} )}^{2} - 2 \times 4 = \frac{16}{9 } - 8 = \\ \frac{16 - 72}{9} = - \frac{56}{9}$

4 0

3 years ago

Last year, a car dealership sold 144 new cars and 108 used cars. Since then, the number of new cars sold is increasing by 8 cars

morpeh [17]

Answer: 4 years

Step-by-step explanation:

144 + 8(4) = 176

108 - 5(4) = 88

88 x 2 = 176

4 0

3 years ago

Increase £854 by 89% Give your answer rounded to 2 DP.

kolezko [41]

Step-by-step explanation:

<u>Step 1: Find the answer</u>

$854 * (1 + 0.89) = x$

$854 * 1.89 = x$

$1614.06 = x$

Answer: $x = 1614.06$

3 0

3 years ago

Min-Jee is planting two rectangular flower beds. One bed is 2.78 feet by 4.81 feet, and the other bed is 2.78 feet by 5.61 feet.

shusha [124]

Answer: $(2.78+4.81)(2.78+5.61)$

Step-by-step explanation:

<h3> The complete exercise is attached.</h3><h3></h3>

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width.

Then, you can notice that it can be obtained by multiplying the dimensions of the rectangle.

Knowing this, you can determine that the total area of the two flowers bed can be obtained by adding the products of their dimensions.

Since one of the rectangular flower bed is 2.78 feet by 4.81 feet and the other bed 2.78 feet by 5.61 feet, you can write the following expression to find the total area (in square feet)of the two beds:

$2.78*4.81 +2.78*5.61$

If you factor out 2.78:

$2.78(4.81 +5.61)$ or $(4.81 +5.61)2.78$

Therefore, the expression that does not represent the total area in square feet of the two beds, is:

$(2.78+4.81)(2.78+5.61)$

6 0

3 years ago

Read 2 more answers