Question

The LCM of three prime numbers are 4991. Find the greatest number between these prime numbers.

Answer 1

Hint : We know that 2 (or) more prime numbers can never have a common factor.
a) Let three prime numbers be \[{\text{x,y,z}}\]
b)As LCM of these numbers is 4991
c)Here LCM of these three prime numbers is the same as that of the product of these prime numbers .

Complete step-by-step answer:
So,
\[\left( {\text{x}} \right){\text{*}}\left( {\text{y}} \right){\text{*}}\left( {\text{z}} \right){\text{ = 4991}}\]
By observation we can conclude that ‘7’ is one of the prime numbers as 4991 is divisible by 7
So,
\[
  {\text{yz = }}\,\dfrac{{{\text{4991}}}}{{\text{7}}} \\
  {\text{yz = 713}} \\
  {\text{yz = 713}} \\
\]
Use hit and trial method to find factor of 731
we can guess that ‘y’ as 23 and z as 31 (or) vice versa

So, the greatest prime number is 31

Note : In these types of questions we need to use our observation ability.
To find 713 factors we can guess by observing its unit digit
Additionally, we should also remember how to find LCM of given numbers.
One of the basic methods is to list out all the multiples of the numbers until you get the first common multiple from the numbers. Ex, LCM of 4 and 10:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28
Multiples of 10: 10, 20, 30, 40
Here, the number 20 is the first common multiple of both 4 and 10. So, the LCM of 4, 10 is 20.