What two numbers has a gcf of 2 and a lcm of 60?

As the least common multiple of two numbers is 60 , the two numbers are factors of 60 . Among {1,2,3,4,5,6,10,12,15,20,30,60} , 3 & 10 and 5 & 12 are the only two pair of numbers whose difference is 7 . But Least common multiple of 3 and 10 is 30 .

Step-by-step explanation:

Two whole numbers have a LCM of 60.

Each number is less than or equal to 12.

The GCF of the two numbers is 2.

What are these two numbers?

Factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Our answers are in there, not greater than 12, and even numbers, so:

2, 4, 6, 10, 12

So let’s check the LCMs:

All of them are multiples of 2.

12 is a multiple of both 4 and 6.

4 and 10 share 20 as a multiple.

6 and 10 share 30.

That leaves 10 and 12 as our two numbers.

5

step-by-step explanation: