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# New question

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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

#1
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The ratio of A to B in not clear to me. Can you clarify it?

Guest Mar 16, 2017
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#1
+5

The ratio of A to B in not clear to me. Can you clarify it?

Guest Mar 16, 2017
#2
+18619
+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

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