Question

The LCM of 6,12 and n is 660. Find all the possible values of n. Explain briefly

Answer 1

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. 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. 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.

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Step-by-step explanation: