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what is the LCM of 8847 and 2532

Guest Feb 18, 2015

Best Answer 

 #2
avatar+20598 
+10

What is the LCM of 8847 and 2532 ?

$$\small{\text{The following formula reduces the problem of computing the least common multiple}}\\
\small{\text{to the problem of computing the greatest common divisor (GCD), }}\\
\small{\text{also known as the greatest common factor:}}\\\\
\small{\text{
$
\boxed{lcm$(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)} }
$
.
}}$$

There is the Euclidean algorithm for computing the GCD.

$$\small{\text{gcd$(8847,2532)$}} \\
\small{\text{$
\begin{array}{rrrr}
& & q & r\\
8847 & 2532 & 3 & 1251 \\
2532 & 1251 & 2 & 30\\
1251 & 30 & 41 & 21\\
30 & 21 & 1 & 9 \\
21 & 9 & 2 & \textcolor[rgb]{1,0,0}{3} \\
9 & 3 & 3 & $ algorithm Ends $ 0
\end{array}
$}}\\\\
\small{\text{gcd$(8847,2532)$}} = 3 \\$$

$$\small{\text{lcm$(8847,2532)=\dfrac{|8847\cdot 2532|}{3} = 7466868 $}}$$

heureka  Feb 18, 2015
 #1
avatar+27223 
0

The LCM of 8847 and 2532 is 7466868

.

Alan  Feb 18, 2015
 #2
avatar+20598 
+10
Best Answer

What is the LCM of 8847 and 2532 ?

$$\small{\text{The following formula reduces the problem of computing the least common multiple}}\\
\small{\text{to the problem of computing the greatest common divisor (GCD), }}\\
\small{\text{also known as the greatest common factor:}}\\\\
\small{\text{
$
\boxed{lcm$(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)} }
$
.
}}$$

There is the Euclidean algorithm for computing the GCD.

$$\small{\text{gcd$(8847,2532)$}} \\
\small{\text{$
\begin{array}{rrrr}
& & q & r\\
8847 & 2532 & 3 & 1251 \\
2532 & 1251 & 2 & 30\\
1251 & 30 & 41 & 21\\
30 & 21 & 1 & 9 \\
21 & 9 & 2 & \textcolor[rgb]{1,0,0}{3} \\
9 & 3 & 3 & $ algorithm Ends $ 0
\end{array}
$}}\\\\
\small{\text{gcd$(8847,2532)$}} = 3 \\$$

$$\small{\text{lcm$(8847,2532)=\dfrac{|8847\cdot 2532|}{3} = 7466868 $}}$$

heureka  Feb 18, 2015
 #3
avatar+94101 
0

Thanks Heureka,

It took me a while to work out what you were doing and it will take me much longer to work out why it works but that is really nifty.

Thank you for showing me.

Melody  Feb 19, 2015

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