LCM

The common multiple of the three numbers is 3276. One number is in this number 63 times, the second 7 times, and the third nine times. What are the numbers?

Final Answer:

a =  52
b =  468
c =  364

Step-by-step explanation:

$$\begin{gathered} n=3276 \\ 3276=2\times 2\times 3\times 3\times 7\times 13=2^2\times 3^2\times 7\times 13 \\ a=n/63=3276/63=52 \end{gathered}$$

$b=n/7=3276/7=468$

$$\begin{gathered} c=n/9=3276/9=364 \\ \text{ Verifying Solution: } \\ 52=2^2\cdot 13 \\ 468=2^2\cdot 3^2\cdot 13 \\ 364=2^2\cdot 7\cdot 13 \\ LCM(52,468,364)=2^2\cdot 3^2\cdot 7\cdot 13=3276 \\ x=LCM(a,b,c)=LCM(52,468,364)=3276 \end{gathered}$$

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