Question

The product of two digit two-numbers is 2700 and their L.C.M is 180,then what is the sum of the two numbers?

Answer 1

Remember the method of finding the LCM using prime factorization.
$180=2\times 2\times 3\times 3\times 5$
So, both the numbers must be made of these prime factors (or 1,180)
$2700=2\times 2\times 3\times 3\times 3\times 5\times 5$


Then the first number be $2\times 2\times 3\times 5=60$ and second number be $3\times 3\times 5=45$ is one pair which can be taken
i.e, $x=60$ and $y=45$

Where $LCM(60,45)=180$

And then ,sum, $x+y=60+45=105$