2021 Fall AMC 12A Problems/Problem 8
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Contents
Problem
Let be the least common multiple of all the integers
through
inclusive. Let
be the least common multiple of
and
What is the value of
Solution 1
By the definition of least common mutiple, we take the greatest powers of the prime numbers of the prime factorization of all the numbers, that we are taking the of. In this case,
Now, using the same logic, we find that
because we have an extra power of
and an extra power of
Thus,
. Thus, our answer is
~NH14
Solution 2
First, we compute . We have
Second, we compute . We have
Therefore, .
Therefore, the answer is .
~Steven Chen (www.professorchenedu.com)
See Also
2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |