Is 120 the smallest number that is divisible by 1 2 3 4 5 and 6?

No, it's 60.

To compute the least common multiple (from here on LCM) of a set on numbers, you have to consider their prime factorization. Then the LCM is composed by all the primes appearing in the factorizations, taken with the largest possible exponent.

Also, we can ignore 1, because every number is divisible by 1, and so it doesn't add anithing to the list.

The prime factorizations are:

So, all the primes appearing in these factorizations are 2,3 and 5. Now we have to decide the exponents:

So, the LCM is given by

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