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

5.5

step-by-step explanation:

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent