Find two pairs of numbers with the given number as their least common multiple. (LCM)
10, 36
60, 105
2 and 5
AAA
1 and 69
Why did the number go to therapy? Because its least common multiple was having an identity crisis!
But let me help you out with your request anyway. For the first pair, we can use 5 and 18 as their least common multiple (LCM) is 10. And for the second pair, we can use 20 and 21 as their LCM is 60. Happy number pair hunting!
To find two pairs of numbers with a given least common multiple (LCM), you can start by factoring the number into its prime factors.
Let's begin with the first example, 10 and 36.
1. Prime factorization:
- 10 = 2 x 5
- 36 = 2^2 x 3^2
2. To find numbers with a least common multiple of 10 x 36 = 360, we can choose different combinations of the prime factors.
For example, we can select the following:
- 2^2 x 3^2 = 4 x 9 = 36
- 2 x 5 = 10
These two pairs of numbers, (36, 10) and (36, 45), have a least common multiple of 360.
Now let's move on to the second example, 60 and 105.
1. Prime factorization:
- 60 = 2^2 x 3 x 5
- 105 = 3 x 5 x 7
2. To find numbers with a least common multiple of 60 x 105 = 6300, we can again choose different combinations of the prime factors.
For example, we can select the following:
- 2^2 x 3 x 5 = 60
- 3 x 5 x 7 = 105
These two pairs of numbers, (60, 105) and (140, 60), have a least common multiple of 6300.
In summary, using the prime factorization of a given number, you can create different combinations of its prime factors to find pairs of numbers with the desired LCM.