(b) Hence, find the LCM of 100 and 120.

To find the least common multiple (LCM) of 100 and 120, start by breaking them down into their prime factors. For 100, the prime factorization is \(2^2 \times 5^2\), and for 120, it is \(2^3 \times 3^1 \times 5^1\). The LCM takes the highest power of each prime factor from both numbers: \(2^3\), \(3^1\), and \(5^2\). So, calculate \(LCM = 2^3 \times 3^1 \times 5^2 = 8 \times 3 \times 25 = 600\). Therefore, the LCM of 100 and 120 is 600! If you thought finding the LCM was just about crunching numbers, think again! This multi-faceted concept applies in everything from scheduling events without overlaps to working with fractions. It’s like organizing your calendar or meal prep so that those tasty dinners show up exactly when they should, making it essential in daily planning! When calculating the LCM, a common mistake is forgetting to take the highest powers of all prime factors. Some people might mistakenly add the factors instead of using multiplication. To avoid this, double-check your prime factorization and make sure you include the maximum exponent for each prime in your final calculation. Remember, it's all about finding the right match!