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Find the least cube number which is exactly divisible by 4 and 6 please explain​

Sagot :

mahanth1112

Answer:

216 (if 0 does not work)

Skills needed: LCM, Cubing

Step-by-step explanation:

1) We need to find the lowest possible cube number which is exactly divisible by 4 and 6.

---> First of all, [tex]0^3=0[/tex], and 0 is perfectly divisible by 4 and 6. But most likely, this case will not count, so we will move on to the next possible case.

2) Instead of trying guess and check or trying every cube number, let's think about it algebraically. When looking at an LCM, use prime factorization.

4 prime factorized is: [tex]2^2[/tex]

6 prime factorized is: [tex]2*3[/tex]

This means that the prime number has to have both these factors in them. When you think about it, the least possible cube would be [tex](2*3)^3[/tex], as you will get a [tex]2*3[/tex] and also [tex]2^3[/tex] is a multiple of [tex]2^2[/tex], which is a factor (meaning that [tex]2^2[/tex] is included as a factor here).

Both 4 and 6 can perfectly divide into the number stated above (which is 216). 4 * 54  = 216, 6 * 36  = 216...

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