Algebraic Expression Least Common Multiple

u15_l1_t3_we1 Algebraic Expression Least Common Multiple

[mikeheth]

Great job. This is the best explanation I've heard on why the prime factors in the LCM form the least common multiple of all three numbers.

[michaelvillanueva]

To find the LCM of expressions in factored form, I pretty much tell my students that they can use this handy-dandy formula to derive one for numeric and/or literal expressions:  (LCM of Expressions) = (common factors with the higher exponent) X (factors not in common).  Say for example I want to find the LCM of these expressions (x+1)(x-4),              x(x+1)^2, and 2x(x-4).  According to the algorithm the LCM is 2x(x+1)(x+1)(x-4).  If I want to verify by letting x = 7 (a prime), then I am looking for the LCM of these numeric expressions 24, 448, and 42 (after substituting).  And then according to the algorithm, the LCM is going to be 2688 (again after substituting).  But this is not right because the LCM is really half this value, 1344.  Now try replacing x by a non-prime like 8 and another prime like 2.  So is the predicted algorithm going to agree with finding the LCM using a basic strategy?

[vionluck]

THANKYOU KHAN FOR BREAKING IT DOWN FOR

[zxrtt]

you're a lifesaver Sal

thanks for breaking it down for me, once again : )

[Rapido]

Because it's factorized. Even though it may appear different with a plus sign, it's still one phrase. When multiplied: x*x=x^2 and x*5=5x.

[wendydinh]

On 4:09 you added •(x+5) to the LCM, because the LCM has to be divisible by (x^2 + 5x). But why can’t it be just 2•2•3•5•x•x? With the x and 5 it can be divisible by 5x and with the two Xs they are divisible by x^2, so why can’t the LCM be that? I’m studying for a huge test for it tomorrow. Thanks.

[kinniexann]

tysm! i also enjoyed your voice cause its similar to a someone :DD

[dancervictory]

UGGGGH! I wish Math would solve its own PROBLEMS!!!

[Thingsonline]

I don't understand about why the 5x is turned into (x+5) could you please explain a little more on that?

[dancervictory]

Is this 9th grade math? I am going to the 9th grade in the fall and I need help....