Teacher2Teacher |
Q&A #4147 |
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I don't know if there is an easy way to get this across, but here are two ideas that might help a little: First, focus on the Last letter rather than the first. Stress that in one case we are looking for factors, and in the other, we are looking for multiples. What are some factors of 12? What are some multiples of 12? This should help... Second... When you teach them to compute LCM and GCF, do them together. A few months ago one of the teachers here wrote an answer about this and I just spent 30 minutes trying to find it, without success, so here is my version of the same thing.. I will use two numbers, three works the same.... Find the GCF and LCM of 24 and 36 At each step, have the students divide out ANY factor that will work in both numbers, and the quotient of each under the original terms Factors 24 36 4 6 9 3 2 3 That is all the numbers that will divide into both numbers. Multiply down the left row and that is the GCF 3*4 = 12 Now start with the 12 and multiply it across the bottom row 12* 2 * 3 = 72.. This is the LCM. After a few runs through this it is the most obvious thing in the world that the LCM is LARGER because you multiplied something times the GCD to get the LCM. Now the least common denominator is just the Least common multiple of the denominators, I would teach it as such. And the Greatest common divisor, if that is what you mean by GCD, is just another name for the greatest common factor. I hope this helps, good luck, and thanks for writing. -Pat Ballew, for the Teacher2Teacher service
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