Investigate GCD and LCM in applications.

• Factor any pair of integers to find their GCD and LCM
• Use the commands gcd and lcm to verify the GCD and LCM of any pair of integers

Finding the greatest common divisor (GCD) and least common multiple (LCM) of two integers is an important skill for calculating the common denominator to add or subtract fractions. For this reason, the learning outcomes listed above are included in virtually all state guidelines. Recently, biologists have discovered that the lcm of the life cycles of an insect species and its predator plays a vital role in that species’ survival. By adjusting its life cycle so it has no factor in common with the life cycle of its main predator, an insect species can increase its chances of survival. As researcher Glenn Webb asserted, "The prime-number life cycle is no coincidence, but has evolved as an effort to avoid predators." In the life cycle of the cicadas (see the discussion in the lesson included here) we see a dramatic application of the lcm in the natural world.

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