Given a universal set = \1, 2, ..., 20\ and sets A, B, C, find the following: c) Set C = Even numbers less than 15, d) A C, e) B C, f) A B C, g) A C.

The numbers in $\Sigma$ less than 15 are $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}$.

Set C is $\boxed{\{2, 4, 6, 8, 10, 12, 14\}}$.

2. d) $A \cap C$

Set A = $\{3, 6, 9, 12, 15, 18\}$
Set C = $\{2, 4, 6, 8, 10, 12, 14\}$

The elements present in both sets are 6 and 12.
$A \cap C = \boxed{\{6, 12\}}$.

2. e) $B \cap C$

Set B = $\{7, 9, 11, 13, 15, 17, 19\}$
Set C = $\{2, 4, 6, 8, 10, 12, 14\}$

There are no common elements between these two sets.
$B \cap C = \boxed{\{\}}$ (or $\emptyset$).

2. f) $A \cap B \cap C$

We know that $B \cap C = \{\}$.

$A \cap B \cap C = A \cap (B \cap C) = A \cap \{\} = \boxed{\{\}}$ (or $\emptyset$).

2. g) $A \cup C$

Set A = $\{3, 6, 9, 12, 15, 18\}$
Set C = $\{2, 4, 6, 8, 10, 12, 14\}$

$A \cup C = \boxed{\{2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 18\}}$.

3. a) Find the L.C.M of 8, 12 and 18

The prime factors are 2 and 3.
Highest power of 2 is $2^3$.
Highest power of 3 is $3^2$.

The L.C.M of 8, 12, and 18 is $\boxed{72}$.

3. b) Find the H.C.F of 36, 48 and 60

The common prime factors are 2 and 3.
Lowest power of 2 is $2^2$.
Lowest power of 3 is $3^1$.

The H.C.F of 36, 48, and 60 is $\boxed{12}$.