In the form of a guide, write numbers 1 to 100.
a. Identify all prime numbers by applying the division rule.
b. Find the common multiple of 4, 5, 6.
Answer (2)
To address your question, we will separate it into two parts: a) Identifying prime numbers from 1 to 100, and b) Finding the common multiple of 4, 5, 6.
Part A: Identifying Prime Numbers from 1 to 100
Prime numbers are numbers that have only two distinct positive divisors: 1 and themselves. To find the prime numbers between 1 and 100, we check each number to see if it is divisible only by 1 and itself.
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
To verify that a number is prime, ensure it is not divisible by any prime numbers less than or equal to its square root.
Part B: Finding the Common Multiple of 4, 5, and 6
To find the least common multiple (LCM) of the numbers 4, 5, and 6, we usually use the prime factorization method:
The prime factorization of 4 is 2 2 .
The prime factorization of 5 is 5 1 .
The prime factorization of 6 is 2 1 × 3 1 .
The LCM is found by taking the highest power of each prime number present in the factorizations:
From 4, take 2 2 .
From 5, take 5 1 .
From 6, take 3 1 .
Now, multiply these together:
L CM = 2 2 × 3 1 × 5 1 = 4 × 3 × 5 = 60
Therefore, the least common multiple of 4, 5, and 6 is 60.
The prime numbers between 1 and 100 include 2, 3, 5, 7, 11, among others, leading up to 97. The least common multiple of 4, 5, and 6 is calculated to be 60. This involves using their prime factorizations and taking the highest powers of the primes present.
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