Question

Answer them all please ​

Answer 1

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.

Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integers

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 maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

a) 12 and 48

First, we factorize each integer:

$12 = 2^{2}\times 3$, $48 = 2^{4}\times 3$

Then the highest common factor and the least common multiple are, respectively:

$LCM = 2^{4}\times 3 = 48$, $HCF = 2^{2}\times 3 = 12$

The highest common factor and the least common multiple are 12 and 48, respectively. $\blacksquare$

b) 24 and 36

First, we factorize each integer:

$24 = 2^{3}\times 3$, $36 = 2^{2}\times 3^{2}$

Then, the highest common factor and the least common multiple are, respectively:

$LCM = 2^{3}\times 3^{2} = 72$, $HCF = 2^{2}\times 3 = 12$

The highest common factor and the least common multiple are 12 and 72, respectively. $\blacksquare$

c) 32 and 40

First, we factorize each integer:

$32 = 2^{5}$, $40 = 2^{3}\times 5$

Then, the highest common factor and the least common multiple are, respectively:

$LCM = 2^{5}\times 5 = 160$, $HCF = 2^{3} = 8$

The highest common factor and the least common multiple are 8 and 160, respectively. $\blacksquare$

d) 24, 48 and 60

First, we factorize each integer:

$24 = 2^{3}\times 3$, $48 = 2^{4}\times 3$, $60 = 2^{2}\times 3 \times 5$

Then, the highest common factor and the least common multiple are, respectively:

$LCM = 2^{4}\times 3 \times 5 = 48$, $HCF = 2^{2}\times 3 = 12$

The highest common factor and the least common multiple are 12 and 48, respectively. $\blacksquare$

e) 42, 56 and 70

First, we factorize each integer:

$42 = 2\times 3 \times 7$, $56 = 2^{3}\times 7$, $70 = 2\times 5\times 7$

Then, the highest common factor and the least common multiple are, respectively:

$LCM = 2^{3} \times 3 \times 5 \times 7 = 840$, $HCF = 2\times 7 = 14$

The highest common factor and the least common multiple are 14 and 840, respectively. $\blacksquare$

To learn more on prime numbers, we kindly invite to check this verified question: brainly.com/question/4184435

Answer 2

Answer:

see the attachment

i hope it helps u ✌️✌️✌️☠️