Name: David

Who is asking: Student
Level: All

Question:
Find the GCD adn LCM of the following numbers. Assume p<q<r and leave answer in exponential form.

2 to the power p, 3 to power q, 5 to power r

and

2 to power q, 3 to power r, 7 to power p

If you find the letters intimidating try some numbers for p, q and r first and then try it with p, q and r as unknowns. For example try p = 7, q = 8, and r = 9. The numbers are then

Since 7 < 8 the highest power of 2 that divides both numbers is 2⁷

Since 8 < 9 the highest power of 3 that divides both numbers is 3⁸

Since 7 < 9 the highest power of 5 that divides both numbers is 5⁷

Thus the greatest common divisor of 2⁷ x  3⁸ x 5⁹ and 2⁸ x 3⁹ x 5⁷is

Now can you see how to do it in general?