The greatest common factor (GCF) is the greatest factor that divides two integers.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{8} \) x \( \frac{4}{9} \) = \( \frac{4 x 4}{8 x 9} \) = \( \frac{16}{72} \) = \(\frac{2}{9}\)

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{5} \) ÷ \( \frac{4}{9} \) = \( \frac{3}{5} \) x \( \frac{9}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{5} \) x \( \frac{9}{4} \) = \( \frac{3 x 9}{5 x 4} \) = \( \frac{27}{20} \) = 1\(\frac{7}{20}\)

The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 have in common.