The least common multiple of two numbers
Is 60 , and one of the numbers is 7 less than
The other number. What are the numbers
Factors of 60
2, 30
3, 20
4, 15
5, 12
6, 10
5 and 12
To find the numbers, we need to set up an equation based on the given information.
Let's assume one of the numbers is "x". Since it is stated that the other number is 7 less than "x", we can represent the other number as "x - 7".
The least common multiple (LCM) of two numbers is the smallest multiple that both numbers share. In this case, the LCM is 60.
Now, we can set up an equation using the LCM and the two numbers:
LCM(x, x - 7) = 60
To solve the equation, we need to find the factors of 60 and check which combination satisfies the condition.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Considering the first number as "x," we can try each of the factors and check if x - 7 is another factor. If it is, we have found our solution.
Trying the factors:
1 is a factor of 60, but (x - 7) - 1 = x - 8, which is not a factor of 60.
2 is a factor of 60, and (x - 7) - 2 = x - 9, which is not a factor of 60.
3 is a factor of 60, but (x - 7) - 3 = x - 10, which is not a factor of 60.
4 is a factor of 60, but (x - 7) - 4 = x - 11, which is not a factor of 60.
5 is a factor of 60, and (x - 7) - 5 = x - 12, which is a factor of 60.
So, x = 12.
Therefore, one number is 12 and the other number is 12 - 7 = 5.