# Math Help - least common multiple

1. ## least common multiple

The LCM of two numbers is 24. Their GCF is 4. The numbers differ by 4. What are the numbers?

2. Originally Posted by coneyfirelady
The LCM of two numbers is 24. Their GCF is 4. The numbers differ by 4. What are the numbers?
Total Numbers = 3
LCM = 24
HCF/GCD = 4

Their numbers are 4, 8, and 12.

3. Originally Posted by coneyfirelady
The LCM of two numbers is 24. Their GCF is 4. The numbers differ by 4. What are the numbers?
For $x,y>0$
We have,
$\gcd(x,y)\cdot \mbox{lcm}(x,y)=xy$
Thus,
$xy=4\cdot 24=96$
Und,
$x-y=4$
Now you can solve.