# The same multiple as before

Number Theory Level 5

For a positive integer $$n$$, we define $G(n) = \mbox{lcm}(1,2,\ldots,n).$ For how many integers $$1 \leq k \leq 100$$ is $$G(k) = G(k+1)?$$

Details and assumptions

You may use the fact that there are 25 primes less than 100.

×