Donna wants to calculate the height of a tree. She finds the length of the tree's shadow is 25 meters and the angle of elevation
from the ground to the top of the tree is 30°. Find the height of the tree to the nearest whole number.
1 answer:
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Consider the prime factorization of 20!.
The LCM of 1, 2, ..., 20 must contain all the primes less than 20 in its factorization, so
where is some integer not divisible by any of these primes.
Compare the factorizations of the remaining divisors of 20!, and check off any whose factorizations are already contained in the product of primes above.
- missing a factor of 2
- ✓
- missing a factor of 2²
- missing a factor of 3
- ✓
- missing a factor of 2
- ✓
- ✓
- missing a factor of 2³
- missing a factor of 3
- missing a factor of 2
From the divisors marked "missing", we add the necessary missing factors to the factorization of , so that
Then the LCM of 1, 2, 3, …, 20 is