How to Find The LCD (Lowest Common Denominator) The EASY WAY

How to Find The LCD (Lowest Common Denominator).

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TC Math Notes

[EY]

When you got to the part where you speak about the LCD Prime Factors, adding exponents, really complicated things. Your comment section is filled with much better suggestions on the easiest steps as your tutorial over complicated things and made me just as confused as I was before.

[CapitalWorksPro]

From a mathematician (not me)

Find a number that your denominators share in common.

20 and 32 share the number 2 in common.

20 ÷ 2 is 10
32 ÷ 2 is 16

10 and 16 also share 2 in common.

10 ÷ 2 is 5
16 ÷ 2 is 8

5 and 8 share 1 in common. Once we get to 1 in common, we stop and multiply all of the numbers on the outside that we found in common, and the last two numbers. Visual aid below to show what we did.


2 |20 & 32

2 | 10 & 16

1 | 5 & 8

2 * 2 * 1 * 5 * 8 = LCD = 160


You'll notice that 20 and 32 also share 4 in common.

20 ÷ 4 is 5
32 ÷ 4 is 8

4 * 1 * 5 * 8 = 160

So long as both denominators actually have the number you choose in common with each other, this will work.

[ryanburnham]

When there is only two fractions, I always just multiply the denominators together, and multiply the numerators by the other denominator. You get a common denominator this way, which is all you need to add/subtract (not the LCD itself as you stated), of course this does lead to reducing the resulting fraction, if you so choose (again no real need as you still have the correct answer but it may be beneficial). Of course if you have several fractions with different denominators, say 10, it may be in your interest to have a "trick" to find the LCD, however you stated this works for trying to find it between two denominators and when I tried it with 5 different denominators I was off by a factor of almost 10. I did still get a common denominator and was able to add them but it wasn't the LCD. My point is that why take all these extra steps and encourage students to take these extra steps early instead of just at the end, reducing a fraction seems like there is less opportunity for error than the process you provided. K.I.S.S. = Keep it Simple Stupid a method I like to use from getting myself in trouble algebraically, or life in general.

[tonywright]

I've said in response to some of your other videos that if I was ever taught your method of using the factor tree to find a LCD, which I doubt, I have forgotten it. This video was excellent. I actually recorded it so that I can review. Maybe it was not a profoundly important mathematical method but I believe it will help me understand other things as I relearn maths. Thank you.

[spudhead]

If you want to skip all the crud he's spouting at the start, jump to 6:27

[Geoff_G]

Anything times 20 ends in zero.
2 times 5 ends in zero.
Therfore:
5×7/32 = 35/160
8×3/20 = 24/160
59/160 answer.

[josgalgebra]

Pick what you need from 2*2*5 and 2*2*2*2*2. The number you need is 2*2*2*2*2*5. This as a regular whole number is 160.

[Vipre-]

Why overcomplicate it? 20 ends in 0 so any whole number multiple will also end in 0, the quickest way to make a number ending in 2 end in a 0 is multiply by 5. 5 times 32 is 160 so the LCD is 160.
Maybe a more complicated problem would've been a better example.

[thomassicard]

I did it a different way that took 5 simple steps. (In fact, two approaches took just 5 steps, neither of which were the exponent involved method.) Apples and oranges... still came out the same answer: 59/160

[meganhoyle-keenan]

This would be so much better and more helpful if you got to the point.

[josgalgebra]

The example should take two minutes or less.

[truuluvv]

Somewhere I got lost, but I also learned some things. Then I finally understood, the point is to find out what "x" is, which you learned from the 32, lol. For me, this isn't so much about learning a technique, but to give my brain some exercise, as it doesn't work like it used to. When you "go on tangents", I listen, and then look up other videos to understand what you mean. I am finding myself appreciating math as a past-time, as entertainment, as a necessary tool, a last-ditch effort to ward off dementia.

[gilbertopatino]

Thank you so much for another great video 🙏👍

[antilogism]

That's a pretty cool method. Thanks!

[thomasharding]

Multiply the two denominators together and divide the results by the LARGEST COMMON FACTOR (LCF) of the denominators. LCF of 20 and 32 is 4. 20 x 32 = 640 and 640 divided by 4 is 160. Still have to factor them but it is less pick-and-choosing and multiplication.

[Astrobrant]

From 6:51 to 11:36 (4 minutes and 45 seconds) you went through a lot of steps, loading lots of stuff to remember and understand onto the student's brain, and lots of opportunities to make mistakes... when all you had to do was show how to extract the greatest common factor and multiply that by the two remaining factors.

By the time you got to 6:58 (9 seconds) you were one step away from the LCD.
4x5 and 4x8 (shown)
Extract the GCF (4) and multiply by 8 and 5. That's 160. DONE!

[davidduncan]

3/20+7/32 is interesting to solve. I simply write the factors in this bow tie multiplication, then I leave the multiplication unsolved until I find another factor that commonly goes into all three of these products. Be careful that your common factor goes into all three products when there is addition or subtraction incolved. Otherwise this method will not work. My work would look like this: (32×3+7×20)/(20×32). I see that the common factor for all three products, shown here, is four. Both of the thirty-twos can become eights and the twenty at the top can become a five. Do NOT touch the twenty on the bottom because that is part of the product of 20×32. After dividing these numbers by four, we should have this: (8×3+7×5)/(20×8). At this point, we can start solving the multiplication: (24+35)/160. The final step is to clean up this addition to get 59/160. Note that 59 is a prime number, so this is the best I can do at getting this fraction down to its lowest numbers.

[tamaramelendez]

Use the GCD-LCM formula to show that in order to add the fractions 3/14 and 6/15 we can do no better than taking a common denominator equal to 210. Nee to show work but I do not understand it. Please help

[GhilDonacin]

This is so confusing im a 6th grader and i need real help i have a test coming up :(

[tiffanyandrews]

Answer is 59/160 . 8* 20=160 and 5*32=160. We add top#24+35=59.