$32 \cdot 23$ Among the first 100 positive integers, the number of integers that can be divided by $2,3,4,5$ is
(A) 0 .
(B) 1 .
(C) 2 .
(D) 3 .
(E) 4 .
(32nd American High School Mathematics Examination, 1981)
[Solution 1] The positive integers not exceeding 100 and divisible by 5 are $5,10,15, \cdots 100$. Among these, only $20,40,60,80$ are divisible by 4.
Among these, only 60 is divisible by 3. Since 60 is divisible by 4, it is naturally divisible by 2.
Therefore, there is only one number that meets the condition.
So the answer is $(B)$.
[Solution 2] The least common multiple of $2,3,4,5$ is 60. Therefore, the numbers that can be divided by $2,3,4,5$ can only be multiples of 60.
Thus, in the range $1 \sim 100$, only 60 meets the requirements of the problem.
So the answer is $(B)$.