FTCE General Knowledge Math Practice Test

What is the result of multiplying 24 and 36 in the context of determining LCM?

1. 600

2. 72

3. 48

4. 60

The correct answer is: 72

To determine the least common multiple (LCM) of two numbers, multiplying those two numbers gives a product that is generally larger than the LCM itself. The formula for finding the LCM of two numbers, \( a \) and \( b \), is to multiply them together and then divide by their greatest common divisor (GCD): \[ LCM(a, b) = \frac{a \times b}{GCD(a, b)} \] In the case of 24 and 36, if you calculate their product, you get 864. The next step is to find the GCD of these two numbers. The GCD of 24 and 36 is 12. When you use the LCM formula: \[ LCM(24, 36) = \frac{24 \times 36}{12} = \frac{864}{12} = 72 \] This shows that the least common multiple of 24 and 36 is indeed 72. Understanding this relationship between multiplication, LCM, and GCD allows for more accurate calculation and comprehension of number theory fundamentals.