What are all of the possible whole number values for $ n $ if the least common multiple of $ n $ and 6 is 42?

Question

SlowZasob · Answer

I did it with "tries & mistakes" method: 
 n is not 1, because LCM of 1 and 6 is 6 n is not 2, because LCM of 2 and 6 is 6 n is not 3, because LCM of 3 and 6 is 6 n is not 4, because LCM of 4 and 6 is 12 n is not 5, because LCM of 5 and 6 is 30 n is not 6, because LCM of 6 and 6 is 6 n might be** 7 **, because LCM of 7 and 6 is what we're looking for - 42. n might be also 14 or 21 - so these are all multiplies of 7 which are less or equal to half of 42. 
 I hope it helps :)

SlowZasob · Answer

The possible whole number values for n for which the LCM of n and 6 equals 42 are 7 , 14 , 21 , and 42 . This conclusion comes from evaluating the LCM condition based on their prime factors. Each of these values was verified to meet the requirement of having an LCM of 42 with 6 . 
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What are all of the possible whole number values for \( n \) if the least common multiple of \( n \) and 6 is 42?

Answer (2)

What are all of the possible whole number values for \( n \) if the least common multiple of \( n \) and 6 is 42?

Answer (2)

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