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Q.

What is the smallest 4-digit number that is divisible by 18, 24 and 32?


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a

1152

b

1552

c

1522

d

1125 

answer is A.

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Detailed Solution

The given numbers are 18, 24 and 32.
To find, the smallest 4-digit number that is divisible by 18, 24 and 32.
Prime factorization of 18, 24, 32 is,
Question ImageHere, 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.
LCM of 18, 24, 32 is 288.
Using the multiples of the LCM value, we can get the smallest four-digit number.
288 × 1 = 288
288 × 2 = 576
288 × 3 = 864
288 × 4 = 1152
Here 1152 is the smallest 4-digit multiple of 288 and it is exactly divisible by 18, 24 and 32.
Therefore, option 1 is correct.
 
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