Two whole numbers have a least common multiple of 60. -Each number is less than or equal to 12. -The greatest common factor of the two numbers is 2. What are the two numbers?

The two number are 10 and 12

Step-by-step explanation:

Two whole numbers have a least common multiple of 60.

We are told that:

-Each number is less than or equal to 12.

The first thing we know is that: one of that two number is 12

The next step would be to find the factors of 60

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 60 that is equal to or less than 12 is

1, 2, 3, 4, 5, 6, 10, 12

We would find which of these number that has the greatest common factor of 2 with 12

The factors of 10 are: 1, 2, 5, 10

The factors of 12 are: 1, 2, 3, 4, 6, 12

Then the greatest common factor is 2...

Also calculating the least common factor of 10 and 12

Multiples of 10:

10, 20, 30, 40, 50, 60, 70, 80

Multiples of 12:

12, 24, 36, 48, 60, 72, 84

Therefore,

LCM(10, 12) = 60

Therefore, two numbers with the least common multiple of 2 and greatest common factor of 60 is 10 and 12

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet