1. **State the problem:** We need to find the number of elements in the intersection of sets $K$, $L$, and $M$, where: - $K$ is the set of multiples of 3. - $L$ is the set of multiples of 4. - $M$ is the set $\{1, 2, 3, \ldots, 39, 40\}$. 2. **Understand the intersection:** The intersection $K \cap L \cap M$ consists of numbers that are multiples of both 3 and 4, and also lie between 1 and 40 inclusive. 3. **Find the common multiples:** Multiples of both 3 and 4 are multiples of the least common multiple (LCM) of 3 and 4. 4. **Calculate the LCM:** $$\text{LCM}(3,4) = 12$$ 5. **Find multiples of 12 in $M$:** These are numbers $\leq 40$ that are multiples of 12. 6. **List multiples of 12 up to 40:** $$12, 24, 36$$ 7. **Count these multiples:** There are 3 such numbers. **Final answer:** $$n(K \cap L \cap M) = 3$$