Question 464757: Suppose K=2^5*7*11, L=2^3*7*11*13, M=2*29^2, and N=4*11*13^2*29. Which is the least common multiple of each of the following (in factored form.)
A. K and L
B. M and N
C. K and M
D. K, L, and N
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! A: If we arrange the factors side by side:
22222 7 11
222 7 11 13
The highest number of 2's is 5, the highest number of 7's, 11's and 13's are 1 each. The LCM of K and L is therefore 2^5*7*11*13.
Try the others the same way. Another way to find the LCM is to think of it as taking the union of two sets; if we visualize K = {2,2,2,2,2,7,11} and L = {2,2,2,7,11,13} then the LCM is the union of the two sets, or {2,2,2,2,2,7,11,13} (elements in either K or L). It's not exactly the same as taking the union of the sets since the 2's are assumed to be distinct, but this method will work.
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