Wednesday, November 4, 2009

Finding the GCF and LCM


After students have mastered Prime Factorization, it is nice to move into finding the Greatest Common Factors and Least Common Multiples of numbers. I like to do this using a Venn Diagram. The Venn Diagram is a nice way to organize all of the information in a really easy to understand way for students. Let's say that you are trying to find the GCF and LCM of the numbers 24 and 52. Use the Composite/Prime line to find the Prime Factorization of each number as described in yesterday's blog. 24 = 2^3 * 3, and 52 = 2^2 * 13. Put the prime factors that 24 and 52 have in common into the intersection portion of the Venn Diagram, and fill in the remaining numbers in the rest of the circle for each number.

The middle portion of the Venn Diagram contains the GCF....(for numbers 24 and 52, that would be 2^2 or 4), and the remaining numbers along with the GCF multiplied together equals the LCM...(for 24 and 52 that would be 2 * 3 * 13 * 4 = 282). Easy to see and do for most students!

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