LCM
Number Theory
Level
3
what is the LCM for number 1,2,3..........20.
Then, divide the answer by half
The answer is 465585120.
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Very easy one.. think it in the powers of prime numbers..
What is the highest power of 2 in numbers from 1- 20. 16 is 2^4
What is the highest power of 3 in numbers from 1- 20. 9 is 3^2 .
What is the highest power of 5 in numbers from 1- 20. 5 is 5^1.
What is the highest power of 7 in numbers from 1- 20. 7 is 7^1.
What is the highest power of 11 in numbers from 1- 20. 11 is 11^1.
What is the highest power of 13 in numbers from 1- 20. 13 is 13^1.
What is the highest power of 17 in numbers from 1- 20. 17 is 17^1.
What is the highest power of 19 in numbers from 1- 20. 19 is 19^1.
==> Now multiply all values, that is 16 9 5 7 11 13 17*19=232792560.
But we need answer divide by 1/2, that means answer multiply by 2. Which is 465585120 .