a) The highest common factor and the least common multiple are 12 and 48, respectively.
b) The highest common factor and the least common multiple are 12 and 72, respectively.
c) The highest common factor and the least common multiple are 8 and 160, respectively.
d) The highest common factor and the least common multiple are 12 and 48, respectively.
e) The highest common factor and the least common multiple are 14 and 840, respectively.
<h3>
Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integers</h3>
In this question we must determine the highest common factor and the least common multiple of two integers.
The highest common factor consists in the <em>maximum</em> product of <em>common</em> <em>prime</em> numbers, of the <em>two</em> numbers that divides it, and the least common multiple consists in the product of <em>prime</em> numbers, common and not, of the <em>two</em> numbers, that creates a product that it is <em>greater or equal to</em> the <em>greater</em> integer.
Now, we proceed to determine the numbers for each case:
<h3>a) 12 and 48</h3>
First, we factorize each integer:
,
Then the highest common factor and the least common multiple are, respectively:
,
The highest common factor and the least common multiple are 12 and 48, respectively.
<h3>b) 24 and 36</h3>
First, we factorize each integer:
,
Then, the highest common factor and the least common multiple are, respectively:
,
The highest common factor and the least common multiple are 12 and 72, respectively.
<h3>c) 32 and 40</h3>
First, we factorize each integer:
,
Then, the highest common factor and the least common multiple are, respectively:
,
The highest common factor and the least common multiple are 8 and 160, respectively.
<h3>d) 24, 48 and 60</h3>
First, we factorize each integer:
, ,
Then, the highest common factor and the least common multiple are, respectively:
,
The highest common factor and the least common multiple are 12 and 48, respectively.
<h3>e) 42, 56 and 70</h3>
First, we factorize each integer:
, ,
Then, the highest common factor and the least common multiple are, respectively:
,
The highest common factor and the least common multiple are 14 and 840, respectively.
To learn more on prime numbers, we kindly invite to check this verified question: brainly.com/question/4184435