Question

Tamara goes for a dental checkup every 6 months and gets her eyesight checked every 8 months. If she visited her dentist and her optician this week, how many months will it be until she visits them both in the same week again?

Short answer

Tamara will visit both her dentist and optician in the same week again in \(24\) months.

Step-by-step solution

List multiples of both numbers

First, we will list the multiples of each number, 6 and 8. Multiples of 6: 6, 12, 18, 24, 30, 36, ... Multiples of 8: 8, 16, 24, 32, 40, 48, ...

Find the least common multiple (LCM)

Now, we need to find the smallest multiple that is common between the multiples of 6 and 8. In this case, the smallest common multiple is 24.

Determine the number of months until both appointments coincide

Since the LCM of 6 and 8 is 24, it means that Tamara's dental checkups and eyesight tests will coincide in the same week after 24 months. Thus, Tamara will visit both her dentist and optician in the same week again in 24 months.

Key concepts

GED Math Practice

If you're preparing for the General Educational Development (GED) tests, math practice is key. The GED tests encompass a range of subjects, including Mathematics, which can challenge your problem-solving and number skills. It is essential to familiarize yourself with the types of questions you might encounter, such as calculating the least common multiple (LCM) of two or more numbers – a concept often applied in real-life scenarios, like scheduling appointments or planning events.

For instance, a common GED math practice problem might involve finding out when two events will coincide, similar to the example given where Tamara wants to determine when she will visit her dentist and optician in the same week again. Through repeated practice of these types of problems, you develop the skills to identify important information, list the necessary steps, and apply mathematical procedures accurately. Regular practice of such problems will not only provide you with the familiarity you need to tackle similar questions on the GED math test but also help you efficiently solve real-world problems.

Math Problem Solving

Math problem solving is a fundamental skill that is not only essential for academic success but also invaluable in day-to-day life. It involves a systematic approach to understand and work through mathematics questions. When faced with the need to calculate when two recurring events will overlap, as with Tamara's visits to her dentist and optician, the process begins with defining what you need to find – in this case, the least number of months until the two appointments fall in the same week again.

Here's how you might structure your approach to this problem: First, identify the frequencies of the recurring events. Then, list out a few multiples of each frequency to discover a common number. Finally, ascertain the first point at which these multiples align. This step-by-step methodology is central to solving math problems effectively and is what students must practice to become proficient in mathematics.

LCM Calculation

The calculation of the least common multiple (LCM) is crucial when dealing with problems that require finding a common period or a synchronized cycle for recurring events. The LCM is the smallest number that is a multiple of two or more numbers. There are various methods for computing the LCM, including listing out the multiples or using prime factorization.

In Tamara's scenario, we list the multiples of her dental (6 months) and eyesight (8 months) checkup intervals. When we find the multiples that both intervals share, we uncover that 24 is the smallest multiple they both have in common. Therefore, the calculation of LCM helps Tamara determine that her appointments will coincide every 24 months. Understanding how to calculate LCM is not just a key component of GED math practice or classroom exercises, but an invaluable intellectual tool for organizing and planning in multiple areas of life.