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Question

Find the smallest number which has is divisible by the first four prime numbers. What is the highest common factor of the first four prime numbers? [3 MARKS]


Solution

Smallest Number: [1 Mark]
Highest Common factor: [2 Marks]

The first four prime numbers are 2, 3, 5, 7.
1 is neither a prime nor a composite number so we will not include that.
Now, all these numbers are prime numbers, so the smallest number possible which is a factor of these numbers is the lowest common multiple of these numbers. 
Since these are all prime numbers, their lowest common multiple is the product of these numbers, which is:
2×3×5×7=210
Hence, 210 is the required number.

The given numbers are prime numbers, so all of them will have the highest common factor equal to 1.

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