Let \( \mathrm{S} \) be the set of first 100 natural number, \( \mathrm{L} \) is the least commo...

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Let \( \mathrm{S} \) be the set of first 100 natural number, \( \mathrm{L} \) is the least common multiple of all the elements in \( \mathrm{S} \),
\( \mathrm{P} \) \( \mathrm{P} \) is the product of all the primes in \( \mathrm{S} \) and \( \mathrm{N} \) is the natural number obtained by the ratio \( \mathrm{L} / \mathrm{P} \), then
(i) find the number of cyphers at the end of \( \mathrm{N} \).
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(ii) find the number of divisors of \( \mathrm{N} \) which are even but not divisible by 4 .
(iii) find the sum of all the odd divisors of \( \mathrm{N} \).
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