Find the least common multiple of these two expressions. 10x6 w4 u7 and 8x8 w5 (the numbers are exponents by the way) Thank-you for the assistance ^^ it is greatly appreciated

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shumbm's profile pic

Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Because the variables are independent, the common multiple must include each variable from both expression, and power of each variable must be not less then in every expression.

The least common multiple has the least possible power for each variable, i.e. maximum from both expressions.

For x, the least possible power is max(6,8)=8. For w max(4,5)=5. For u max(7,0)=7.

And the constant factors, 10 and 8, also require least common multiple. It is 40 (10=2*5, 8=2^3, LCM=2^3*5).

(the sign ^ is for the power (exponent))

So the answer is 40*x^8*w^5*u^7.

The greatest common factor, if you need it also, is 2*x^6*w^4 (take min of the powers).

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

This is simple 

Factor of `10*x^6 *w^4 *u^7`

= `10*x^6 *w^4 *u^7`


= `(2 )*( 5)*x^6 *w^4 *u^7` --------------------(1)


Factor of `8*x^8 *w^5`


= `8*x^8 *w^5`


= `(2 )* (2) * (2)*x^8 *w^5` --------------------------(2)

so GCD(greatest common factor) can be easily found by just taking the common terms of (1) and (2)

so,

GCD = `2*x^6 *w^4` -------------------------(3)

As we know the relation ship between GCD and LCM is ,

the product of the two numbers a,b is equal to the product of GCD(a,b) and LCM(a,b)

=>  `a*b = GCD(a,b) * LCM(a,b)`

=> LCM(a,b) = `(a*b)/(GCD(a,b))`

so here, let "a" be the expression (1) and "b" be the expression (2)

then ,LCM is

 LCM = `((10*x^6 *w^4 *u^7)*(8*x^8 *w^5))/(GCD)`

[  From expression (3) we get the value of GCD of (1) and(2)]        

=`((10*x^6 *w^4 *u^7)*(8*x^8 *w^5))/(2*x^6 *w^4 )`

       = `40*x^8 * w^5 * u^7`

is the LCM of (1) & (2) expressions

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