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What is the GCF and LCM of 34 and 784? 

SmartMathMan  Oct 25, 2018
 #1
avatar+372 
+9

I typed GCF(34,784) into my calculator, and got \(\boxed 2\) as my GCF.

 

I did the same for the LCM and got  \(\boxed{13328}\).

 

http://www.mathematicsmagazine.com/applications/GCF_LCM.htm

 

You can use this to find both of them if you do not have a calculator that can calculate GCF and LCM.

KnockOut  Oct 25, 2018
 #2
avatar+372 
+9

The Greatest Common Factor

 

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:

List the prime factors of each number.

Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

 

The Least Common Multiple

 

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

KnockOut  Oct 25, 2018
 #3
avatar+20105 
+2

What is the GCF and LCM of 34 and 784? 

 

\(\begin{array}{|rcll|} \hline 34 &=& 2^1\cdot 17^1 \cdot (7^0) \\ 784 &=& 2^4\cdot 7^2 \cdot (17^0) \\\\ && \begin{array}{|rcll|} \hline \text{gcf}(34,784) &=& 2^1\cdot 17^0 \cdot 7^0 \quad & | \quad \text{min exponent} \\ &=& 2\cdot 1 \cdot 1 \\ &=& \mathbf{2} \\\\ \text{lcm}(34,784) &=& 2^4\cdot 17^1 \cdot 7^2 \quad & | \quad \text{max exponent} \\ &=& 16\cdot 17 \cdot 49 \\ &=& \mathbf{13328} \\ \hline \end{array}\\ \hline \end{array}\)

 

laugh

heureka  Oct 25, 2018

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