Let P represent the set of all natural numbers from 1 to 100, each of which differs from the sum of its factors by 1, and let Q represent the set of all natural numbers from 1 to 100, each of which is equal to the number of its factors. The L.C.M. of the greatest element of P and the greatest element of Q is
Question
Let P represent the set of all natural numbers from 1 to 100, each of which differs from the sum of its factors by 1, and let Q represent the set of all natural numbers from 1 to 100, each of which is equal to the number of its factors. The L.C.M. of the greatest element of P and the greatest element of Q is
Solution
To solve this problem, we first need to find the greatest elements of sets P and Q.
- Set P: The set of all natural numbers from 1 to 100, each of which differs from the sum of its factors by 1.
The factors of a number are the numbers that divide it exactly. For example, the factors of 6 are 1, 2, 3, and 6. The sum of these factors is 12. But 6 does not differ from 12 by 1, so 6 is not in set P.
By checking the numbers from 1 to 100, we find that the greatest number that fits this condition is 2. The factors of 2 are 1 and 2, and the sum of these factors is 3, which differs from 2 by 1.
- Set Q: The set of all natural numbers from 1 to 100, each of which is equal to the number of its factors.
Again, by checking the numbers from 1 to 100, we find that the greatest number that fits this condition is 1. The only factor of 1 is 1 itself.
- The least common multiple (L.C.M.) of the greatest elements of P and Q:
The L.C.M. of 2 and 1 is 2.
So, the L.C.M. of the greatest element of P and the greatest element of Q is 2.
Similar Questions
Find the number of elements in P U QP U Q, if set PP comprises all multiples of 44 less than 200200 and Set QQ comprises all odd multiples of 33 less than 100100.
Which group of numbers is ordered from least to greatest? A. 250,100250,000246,263 B. 246,263250,100250,000 C. 250,100246,263250,000 D. 246,263250,000250,100
Consider the set S of all four-digit natural numbers greater than 9000, each having exactly 16 factors. If the prime factorization of each element in S is the product of powers of only two distinct prime numbers, the sum of all elements in S is________
Provided S - a set of n integers S = s1, s2, ..., sn. Check whether it is possible to divide S into two parts: s1, s2, ..., si and si+1, si+2, ..., sn (1 <= i < n) Remember that the first part is strictly decreasing while the second is strictly increasing one.Input FormatIn the first line you are given an integer 2<=n<=100 and in the following line n integers -100 <= si <= 100.Constraints2<=n<=100 -100 <= si <= 100Output FormatOne word Yes or No.Sample Input 05 -1 2 -1 1 -1Sample Output 0No
Find three positive numbers whose sum is 100 and whoseproduct is a maximum
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.