AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Organizations belong to NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
The following calculation can be used to determine the least common multiple (lcm) of two fractions by dividing the denominators of the fractions by thier greatest common divisor (gcd):
See the following: http://en.wikipedia.org/wiki/Least_common_multiple
Example: 3/4 and 5/12
(4 X 12)/ 4 (gcd of 4, 12) = lcd 12
Using this same method to find the lcm for 3 denominators produces some mixed results.
Example: 1/2, 2/3, and 4/5 Find the lcm:
(2 X 3 X 5)/gcd 1 = lcm 30, but with the fractions 1/2, 3/4, and 5/6, the calculation provides (2 X 4 X 6)/gcd 2 = 24, but 12 is the lcm for these three denominators not 24.
Can you explain why the method/calculation works with two denominators but not generally with three or more denominators, or have I made an error somewhere with my calculations?
I thank you for your reply.
Answer Hello,
The reason it does not work (in general) with more
than 2 denominators is because each denominator
*may* have the same common factor...and when we
multiply them (in the numerator) we *may* be having
multiple factors of the GCD which will not be
"divided out" by the denominator.
For example, with 1/2, 3/4, and 5/6:
there is a GCD of 2...so when we multiply
2, 4, and 6...we are multiply the 2 three times,
but only "dividing it out" once!!!
