SOLUTION: Consider the integers m=2^3*3^2*5^3*7^4*11^2*13^5*17^4 and n=2^5*7^8*19^9. 1.) Note that 2^3 is a factor of both m and n. Show that 2^3 is a factor of m+n. 2.) Determine the G

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Question 1192332: Consider the integers m=2^3*3^2*5^3*7^4*11^2*13^5*17^4 and n=2^5*7^8*19^9.
1.) Note that 2^3 is a factor of both m and n. Show that 2^3 is a factor of m+n.
2.) Determine the GCF and LCM of m and n. (explain reasoning)
3.) Show that GCF(m,n) is a factor of LCM(m,n).

Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Question #1
Distributive Property in the reverse direction; to factorize

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 and 



That's because 

a.  3 is the smaller power of the common prime factor 2.
b.  4 is the smaller power of the common prime factor 7.



That's because

a.  5 is the larger power of the common prime factor 2.
b.  8 is the larger power of the common prime factor 7.
c.  all the other factors of both numbers are included.

3.)  is a factor of 

because a smaller power of a prime is always a factor of a
larger power of the same prime.

Edwin


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