Question

The LCM of 6,12andn is 660.find all possible values of n

Answer 1

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. $2^{0}$ × $3^{0}$ × 5 × 11.

2. $2^{0}$ × 3 × 5 × 11.

3. 2 × $3^{0}$ × 5 × 11.

4. 2 × 3 × 5 × 11.

5. 2² × $3^{0}$ × 5 × 11.

6. 2² × 3 × 5 × 11.

The combination we got is from 2 * 3 = 6.

Answer 2

Answer:

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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