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Find the Lcm of 32,84,180

Guest Sep 9, 2014

Best Answer 

 #1
avatar+20009 
+8

Find the Lcm of 32,84,180 ?

Least Common Multiple, you need the prime factorization:

$$\mbox{prime factorization} \\\\
\begin{array}{rccccc}
32 =& 2^{\textcolor[rgb]{1,0,0}{5}}\ *& 3^0 \ *& 5^0 \ *& 7^0\\
84 =& 2^2 \ *& 3^1 \ *& 5^0 \ *& 7^{\textcolor[rgb]{1,0,0}{1}}\\
180 =& 2^2 \ *& 3^{\textcolor[rgb]{1,0,0}{2}} \ *& 5^{\textcolor[rgb]{1,0,0}{1}} \ *& 7^0\\
\hline
\mbox{in each case the biggest exponent}
& 2^{\textcolor[rgb]{1,0,0}{5}}
\ *& 3^{\textcolor[rgb]{1,0,0}{2}}
\ *& 5^{\textcolor[rgb]{1,0,0}{1}}
\ *& 7^{\textcolor[rgb]{1,0,0}{1}} &= 10080 \\
\end{array}$$

LCM of 32, 84, 180 is 10080

10080 = 315 * 32

10080 = 120 * 84

10080 = 56 * 180

heureka  Sep 9, 2014
 #1
avatar+20009 
+8
Best Answer

Find the Lcm of 32,84,180 ?

Least Common Multiple, you need the prime factorization:

$$\mbox{prime factorization} \\\\
\begin{array}{rccccc}
32 =& 2^{\textcolor[rgb]{1,0,0}{5}}\ *& 3^0 \ *& 5^0 \ *& 7^0\\
84 =& 2^2 \ *& 3^1 \ *& 5^0 \ *& 7^{\textcolor[rgb]{1,0,0}{1}}\\
180 =& 2^2 \ *& 3^{\textcolor[rgb]{1,0,0}{2}} \ *& 5^{\textcolor[rgb]{1,0,0}{1}} \ *& 7^0\\
\hline
\mbox{in each case the biggest exponent}
& 2^{\textcolor[rgb]{1,0,0}{5}}
\ *& 3^{\textcolor[rgb]{1,0,0}{2}}
\ *& 5^{\textcolor[rgb]{1,0,0}{1}}
\ *& 7^{\textcolor[rgb]{1,0,0}{1}} &= 10080 \\
\end{array}$$

LCM of 32, 84, 180 is 10080

10080 = 315 * 32

10080 = 120 * 84

10080 = 56 * 180

heureka  Sep 9, 2014

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