The LCM of 6, 12 and n is 660. Find all possible values of n.
Answers
Answer:
$$\begin{lgathered}n= 55\\\\n= 110\\\\n= 220\\\\n=165\\\\n= 330\\\\n= 660\end{lgathered}$$
Step-by-step explanation:
The first step is to descompose the numbers 6,12 and 660 into their prime factors:
$$\begin{lgathered}6=2*3\\\\12=2*2*3=2^2*3\\\\660=2*2*3 *5 * 11=2^2*3*5*11\end{lgathered}$$
Since, by definition, the Least Common Multiple (L.C.M) is the product of the common and non common prime factors with their highest exponents, we can determine that the possible values of "n" are:
$$\begin{lgathered}n=11* 5 = 55\\\\n=11*5*2 = 110\\\\n=11*5*2^2= 220\\\\n=11*5*3=165\\\\n=11*5* 3*2= 330\\\\n=11*5*3*2^2 = 660\end{lgathered}$$
Answer:
I hope this helps you
Step-by-step explanation:
First of all find out the factors of 660 itself.
660 = 2² × 3 × 5 × 11
We know, the factors of 6 are 2 × 3 & 12 are 2² × 3.
So, definitely, (5 × 11) belongs to n.
Therefore, trying to formulate the indices of 2 and 3 to compute the range we get,
n can be any of the below:
1. × × 5 × 11.
2. × 3 × 5 × 11.
3. 2 × × 5 × 11.
4. 2 × 3 × 5 × 11.
5. 2² × × 5 × 11.
6. 2² × 3 × 5 × 11.
The combination we got is from 2 * 3 = 6.
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