If the least common multiple of A and B is 1575, and the ratio A of B to 3 is 7 , then what is their greatest common divisor?

tertre
Mar 16, 2017

#2**+5 **

**If the least common multiple of A and B is 1575, and the ratio A of B to 3 is 7 ,**

**then what is their greatest common divisor?**

\(\begin{array}{rcll} \hline lcm(a,b) = 1575 &=& 3^2\times 5^2\times 7 \\ \hline \end{array} \)

\(\begin{array}{rcll} a &=& 3^2\times 5^2 \\ b &=& 3\times 5^2 \times 7 \\\\ \dfrac{a}{b} = \dfrac{3^2\times 5^2}{3\times 5^2 \times 7 } &=& \dfrac{3}{7}\\ \end{array} \)

\(\begin{array}{rcll} gcd(a,b) &=& 3\times 5^2 \times 7^0 = 75 \\ \end{array}\)

heureka
Mar 16, 2017