The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 the greatest factor 40 and 68 have in common.

To subtract these radicals together their radicands must be the same:

9\( \sqrt{45} \) - 2\( \sqrt{5} \)
9\( \sqrt{9 \times 5} \) - 2\( \sqrt{5} \)
9\( \sqrt{3^2 \times 5} \) - 2\( \sqrt{5} \)
(9)(3)\( \sqrt{5} \) - 2\( \sqrt{5} \)
27\( \sqrt{5} \) - 2\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (5 + 2) ÷ 3 x 4 - 2²
P: 3 + (7) ÷ 3 x 4 - 2²
E: 3 + 7 ÷ 3 x 4 - 4
MD: 3 + \( \frac{7}{3} \) x 4 - 4
MD: 3 + \( \frac{28}{3} \) - 4
AS: \( \frac{9}{3} \) + \( \frac{28}{3} \) - 4
AS: \( \frac{37}{3} \) - 4
AS: \( \frac{37 - 12}{3} \)
\( \frac{25}{3} \)
8\(\frac{1}{3}\)

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

\( \frac{2}{7} \) ÷ \( \frac{4}{6} \) = \( \frac{2}{7} \) x \( \frac{6}{4} \)

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

\( \frac{2}{7} \) x \( \frac{6}{4} \) = \( \frac{2 x 6}{7 x 4} \) = \( \frac{12}{28} \) = \(\frac{3}{7}\)

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.