If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24
II. 36
III. 48
Choose the correct choice.
A) I only B) II only C) I and II only D) II and III only E) I, II, and III
y needs to be divisible by 3, 8 and 12. This means that it must be the LCM of 3, 8 and 12 or a multiple of the LCM. The LCM is the smallest number which is divisible by all 3 numbers.   LCM of 3, 8 and 12 will be 3*8= 
<gadget id="calculator">3*8</gadget>
<output>24</output>
24   Now y must be either 24 or a multiple of 24. In any case it will always be divisible by 24.   Will it be divisible by 36 necessarily? No. Say if y is 24, it will not be divisible by 36.   Will it be divisible by 48 necessarily? No. Say if y is 24, it will not be divisible by 48.   I onlynswer (I only)
<result>A</result>
If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24
II. 36
III. 48