# As a vaccine scientist, you are required to test your newly developed vaccine in two different populations, populations

As a vaccine scientist, you are required to test your newly developed vaccine in two different populations, populations Xand Y to ensure the safety and effectiveness of the vaccine. There are 3190 subjects from database X and 6094 subjects from database Therefore, you must select a number of subjects from populations X and Y to form a group. The newly formed of group must consist of subjects from both populations without repetition. The maximum number of groups which can be formed is denoted as d.
(1) Use Euclidean algorithm to find $d=GCD\left(X,Y\right).$
2) Find the integers s and tsuch that $d=sX+tY$
3) With the answer obtained from a, what is the ratio of subjects selected from population
4) Find Least Common Multiple for

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Given:
$X=3190$ and
$Y=6094$
(1) Set up a division problem where a is larger than $b.a÷b=c$ with remainder R. Then replace a with b, replace b with R and repeat the division. Continue the process until $R=0$
$6094=1×3190+2904$
$3190=1×2904+286$
$2904=10×286+44$
$286=6×44+22$
$44=2×22+0$
When remainder $R=0$, the GCD is the divisor, b, in the last equation. $GCD=22$
$GCD\left(3190,6094\right)=22$
(2) Finding linear combination of 3190 and 6094
$22=3190\left(128\right)+6094\left(-67\right)$

$\left(3\right)\frac{{P}_{x}}{{P}_{y}}=\frac{3190}{6094}÷\frac{22}{22}=\frac{145}{277}$
(4) LCM of 3190 and 6094
$3190=2×5×11×29$
$6094=2×11×277$
Multiply each factor the greatest number of times it occurs in either 3190 or 6094
$=2×5×11×29×277$
$=883630$
Thus, LCM is 883630