The LCM of 5 and 8 is .

40

Step-by-step explanation:

find a common multiple of 5 and 8 and the least common is 40

40

Step-by-step explanation:

LCM = Lowest Common Multiple

Write down the prime factors of 5 and 8; you could use the factor tree method.

5 is a prime factor

8 = 2,2,2 (2^3)

There's non in common; No 5 within the prime factors of 8, no 2 within the prime factors of 5 (because 5 is a prime factor). So we multiply all of these together!

So 2 x 2 x 2 x 5 = 40

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4