Question

Greatest Common Divisor of two numbers is 8 while their Least
Common Multiple is 144. Find the other number if one number is 16.

Answer 1

Gcd x LCM = product of no’s
144x 8 = 16x ( x = unknown no)
1152 = 16x
x = 72

Pl pl mark me brainliest bro

Answer 2

Given:

Greatest Common Divisor of two numbers is 8 while their Least  Common Multiple is 144.

To Find:

Find the other number if one number is 16.

Solution:

If the LCM( least common multiple) and HCF or GCD( greatest common divisor ) of two numbers are given then we can express these four variables in a relationship which goes as,

$Product =LCM*HCF$

So if the product of two numbers is given and the LCM and HCF of the numbers are also given then we can find either of the numbers if the other number is known, this formula can be understood by the process for which we find the LCM or HCF when we find the LCM we take the highest power of every prime number and multiply them together and in HCF we take the highest power of the only common prime numbers, and it is evident that if we will multiply the LCM and HCF together we will get the product of the numbers we used to find the LCM and HCF.

Now putting all the values, we have,

$Product=LCM*HCF\\16*x=8*144\\x=72$

Hence, the other number is 72.