Find two pairs of numbers with the given number as their least common multiple. (LCM)

10 36

60 105

what help was this

To find two pairs of numbers with a given number as their least common multiple (LCM), we need to find two sets of numbers that when their LCM is calculated, give us the given number.

1) Let's find the first pair of numbers with LCM 10. The LCM of two numbers can be found by multiplying the numbers and dividing it by their greatest common divisor (GCD).

Since we need the LCM to be 10, we can select any two numbers whose product is 10 and whose GCD is 1. One such pair is (2, 5) because GCD(2,5) = 1 and 2 * 5 = 10.

So the first pair of numbers with LCM 10 is (2, 5).

2) Now let's find the second pair of numbers with LCM 36.

Similar to the first case, we need two numbers whose product is 36 and whose GCD is 1. One such pair is (4, 9) because GCD(4,9) = 1 and 4 * 9 = 36.

So the second pair of numbers with LCM 36 is (4, 9).

Therefore, the two pairs of numbers with the given LCMs are:

Pair 1: (2, 5) with LCM 10.
Pair 2: (4, 9) with LCM 36.

Moving on to the second part:

3) Let's find the first pair of numbers with LCM 60.

To find a pair of numbers whose LCM is 60, we need to find two numbers whose product is 60 and whose GCD is 1. One such pair is (10, 6) because GCD(10,6) = 2 and (10/2) * (6/2) = 5 * 3 = 15 * 2 = 30 * 2 = 60.

So the first pair of numbers with LCM 60 is (10, 6).

4) Now let's find the second pair of numbers with LCM 105.

We need two numbers whose product is 105 and whose GCD is 1. One such pair is (7, 15) because GCD(7,15) = 1 and 7 * 15 = 105.

So the second pair of numbers with LCM 105 is (7, 15).

Therefore, the two pairs of numbers with the given LCMs are:

Pair 1: (10,6) with LCM 60.
Pair 2: (7, 15) with LCM 105.

Hope this helps!