What is the smallest multiple of 36 and 24?

The smallest multiple of 36 and 24 is their least common multiple (LCM). To find the LCM, we can use the prime factorization method. The prime factors of 36 are (2^2 \times 3^2) and for 24, they are (2^3 \times 3^1). The LCM takes the highest powers of all prime factors, which gives us (2^3 \times 3^2 = 72). Therefore, the smallest multiple of 36 and 24 is 72.