Multiple choice

If the LCM of first 20 natural numbers is x, then find the LCM of first 25 natural numbers.

  1. 125x

  2. 23x

  3. 115x

  4. 65x

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

LCM(1-20) = x. To get LCM(1-25), we need to multiply x by the prime factors of 21, 22, 23, 24, 25 that are not already covered. 21=3*7 (covered), 22=2*11 (covered), 23=23 (new), 24=2^3*3 (covered), 25=5^2 (5 is covered, but one more 5 is needed). So LCM(1-25) = x * 23 * 5 = 115x.

AI explanation

The LCM of the first 20 natural numbers includes the highest powers of primes up to 20, which are 16, 9, 5, 7, 11, 13, 17, and 19. The LCM of the first 25 natural numbers must also include 23, as well as 25 instead of 9. Dividing the new LCM by x gives 23 multiplied by 25 divided by 9. Since 25 divided by 9 is 25 ninths, the result is 115.

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