Question : The highest common factor of 108, 72, and 5$a$ is $a$. What can be the least common multiple of 108, 72, and $a$?
Option 1: 432
Option 2: 324
Option 3: 108
Option 4: 216
Correct Answer: 216
Solution :
The highest common factor (HCF) of 108, 72, and 5$a$ is given as $a$. This means $a$ is a factor of 108, 72, and 5$a$.
Since '$a$' is a factor of 108 and 72, then $a$ must be a divisor of the HCF of 108 and 72.
Now, the HCF of 108 and 72 is 36.
So, $a$ could be any factor of 36.
The least common multiple (LCM) of 108, 72, and $a$ would be the LCM of 108, 72 (since 'a' is a factor of both 108 and 72) which is 216.
So, the least common multiple of 108, 72, and $a$ is 216.
Hence, the correct answer is 216.
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