For numbers 10-13 find 2 pairs of numbers with the given number as their least common multiple.
10. 10
11. 36
12. 60
13. 105
To find pairs of numbers with a given number as their least common multiple, we need to break down the numbers into their prime factors and then combine the factors in such a way that the least common multiple is equal to the given number.
Let's go through each of the numbers:
10:
The prime factorization of 10 is 2 * 5.
To find pairs of numbers with 10 as their least common multiple, we need to combine the prime factors of 10, which are 2 and 5. One possible pair is 2 * 5 = 10. So the pair is (2, 5).
11:
The prime factorization of 11 is 11 itself.
In this case, since the number is prime, the only pair with 11 as the least common multiple is (11, 1).
36:
The prime factorization of 36 is 2 * 2 * 3 * 3.
To find pairs of numbers with 36 as their least common multiple, we need to combine the prime factors of 36. One possible pair is 2 * 2 * 3 * 3 = 36. So the pair is (2 * 2 * 3, 3).
60:
The prime factorization of 60 is 2 * 2 * 3 * 5.
To find pairs of numbers with 60 as their least common multiple, we need to combine the prime factors of 60. One possible pair is 2 * 2 * 3 * 5 = 60. So the pair is (2 * 2 * 3, 5).
105:
The prime factorization of 105 is 3 * 5 * 7.
To find pairs of numbers with 105 as their least common multiple, we need to combine the prime factors of 105. One possible pair is 3 * 5 * 7 = 105. So the pair is (3 * 5, 7).
In summary, the pairs of numbers with the given numbers as their least common multiple are:
- For 10: (2, 5)
- For 11: (11, 1)
- For 36: (2 * 2 * 3, 3)
- For 60: (2 * 2 * 3, 5)
- For 105: (3 * 5, 7)