Did you know?
Did you know that by using prime factorizations, we can determine the customer who will be the first to receive both types of gift cards at a music store? Let's break it down: Every 20th customer receives a $5 gift card, which means they can be represented as a multiple of 20 (2² × 5). Similarly, every 50th customer receives a $10 gift card, which can be represented as a multiple of 50 (2 × 5²). To find the customer who will receive both types of gift cards, we need to identify the least common multiple (LCM) of 20 and 50 using their prime factorizations. The LCM is given by multiplying the highest powers of all prime factors. In this case, the LCM of 20 (2² × 5) and 50 (2 × 5²) is 2² × 5² = 100. Hence, the 100th customer will be the first to receive both a $5 and a $10 gift card!