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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)

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Part A:
The HCF is an acronym for Highest Common Factor. An unknown number and 63 have an HCF equal to 9. The factors of 63 are 9 and 7. There are lots of numbers to which the HCF with 63 is 9. These should be divisible by 9 but not by 7. That being said, the answers could be 9, 18, 27, etc.

Part B:
LCM is the acronym for least common multiple. Given that the LCM of a number and 48 is 144, the other number could be determined by dividing 144 by 48. If we let x be the number, 
           x = 144/48
           x = 3

Answer:

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 = [tex]\frac{144}{48}=3[/tex]

Now the two numbers may be 3, 6

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