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