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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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Distrubutive property<br> (m-3)(-10)?
mrs_skeptik [129]

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Step-by-step explanation:

<u>Given expression</u>

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4 0
3 years ago
Set D is the set of positive two-digit even numbers less than 25 that do not contain the digit 0.
gavmur [86]

The required set of positive two-digit even numbers less than 25 that do not contain the digit 0 is 12,14,16,18,22,24.

<h3>What is integer?</h3>

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

Set D is the set of positive two-digit even numbers less than 25 that do not contain the digit 0.

According to given question we have

2-digit numbers are the numbers that have two digits and they start from the number 10 and end on the number 99.

Starting at 12 going up the two digit numbers even numbers less than 25 that do not contain the digit 0.

12,14,16,18,22,24

Therefore, the required set of positive two-digit even numbers less than 25 that do not contain the digit 0 is 12,14,16,18,22,24.

Learn more details about integer here:

brainly.com/question/15276410

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4 0
1 year ago
Addison earn $25 mowing her neighbor's lawn then she loaned her friend $18 and got 50 from her grandmother for her birthday she
yarga [219]

Solution: The total money did addison have to begin with is $29.

Explanation:

Let the addison begin with money $x.

It is given that the addison earn $25 from his neighbor and $50 from her grandmother. So total money addison has \$x+\$25+\$50=\$x+\$75

She loaned her friend %18.

Now she has \$x+\$75-\$18=\$x+\$57

It is given that she had $86.

\$x+\$57=\$86\\\$x=\$86-\$57\\\$x=\$29

Therefore, the total money did addison have to begin with is $29.

4 0
3 years ago
Read 2 more answers
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