Question

The sum and the difference between the LCM and GCF of two numbers is 252 and 180, respectively. Find the numbers if one of them is more than twice the other.

Answer 1

Answer:

36 and 216

Step-by-step explanation:

Let  x and y be LCM and GCF respectively.

We are told that the sum and the difference between the LCM and GCF of two numbers is 252 and 180.

Upon using our information we will get a system of equations.

$x+y=252..(1)$

$x-y=180..(2)$

We will use substitution to solve this system of equations.

$x=180+y$

$180+y+y=252$

$2y=252-180$

$2y=72$

$y=\frac{72}{2} =36$  

Now let us find x using equation 1,

$x=252-36=216$

Therefore, LCM is 216 and GCF is 36.

Let a and b our numbers. Now let us find numbers using this information.

We are given that one of them is more than twice the other.

$a>2b$

There can be several such numbers. 36 and 216 can also be numbers. Let us check these numbers.

LCM of 36 and 216 is 216 and GCF is 36 and it satisfies our condition that $a>2b$  because 216 is more than twice 36.

Therefore, our numbers will be 36 and 216.