It is known that the h. c.f. of a given number and 63 is 9. find two possible values of the given number. (with steps if available)

it is known that the l. c.m. of a given number and 48is 144. find two possible values of the given number. (with steps if available)

Step-by-step explanation:

A. Highest common factor is a highest common number of two or more than two numbers, that can exactly divide these numbers.

If H.C.F. of a give number and 63 is 9 then two possible numbers apart from 63 will be multiple of 9.

Like 9, 18, 27, 63 each are divisible by 9.

In other words,

factors of 9 = 1×3×3

factors of 18 = 1×2×3×3

factors of 63 = 1×3×3×7

Now we find the common factors of these numbers as 1×3×3

So the highest common factors of these numbers will be = 9

And the numbers apart from 63 may be 18 and 27.

B. Least common multiple of two or more numbers is the smallest number that is a multiple of all numbers.

Let two numbers are 14 and L

Then common factors of 48 = 1×2×2×2×2×3

and common factor of L = 1×L

Now Least common multiple of these numbers will be = 1×2×2×2×2×3×L

= 48L

As L.C.M. of these numbers is given as 144

So 48L = 144

L =

Now the two numbers may be 3, 6

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05