Discussion

The smallest four-digit number which is a multiple of 6, 7 and 4 is :

Answer: B

The smallest four-digit multiple of 6, 7 and 4 is 1008.

A number divisible by all three must be a multiple of their LCM. With \(6 = 2 \times 3\), \(4 = 2^{2}\) and 7 prime:

\[ \text{LCM} = 2^{2} \times 3 \times 7 = 84 \]

The smallest four-digit number is 1000, and \(1000 \div 84 = 11\) remainder 76, so the next multiple of 84 is

\[ 84 \times 12 = 1008 \]

The other options fail: 1000 is divisible by 4 but not by 3 or 7, 1006 is not divisible by 3, 4 or 7, and 1002 is divisible by 6 but not by 4 or 7.

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