GCF of two numbers is 6 and their LCM is 420 if one of the numbers is 60 then find second number
let the two numbers be 6x and 6y
given: 6x = 60, so x = 10
we know 420 ÷ 60 = 7, which makes the other number 42
check:
60 = 2*2*3*5
42 = 2*3*7
GCF = 2*3 = 6
HCM = 2*2*3*5*7 = 420
To find the second number, we can use the relationship between the Greatest Common Factor (GCF), the Least Common Multiple (LCM), and the numbers themselves.
We know that the GCF of the two numbers is 6 and the LCM is 420. Let's call the second number "x".
The relationship between the GCF, the LCM, and the numbers is as follows:
GCF * LCM = Product of the two numbers
So we can write the equation as:
6 * 420 = 60 * x
Now, let's solve for x by dividing both sides of the equation by 60:
6 * 420 / 60 = x
We get:
420 / 10 = x
42 = x
Therefore, the second number is 42.
To find the second number, we can use the relationship between the GCF (Greatest Common Factor) and the LCM (Least Common Multiple) of two numbers.
Let's denote the two numbers as A and B.
Given that the GCF of A and B is 6, we know that both A and B are divisible by 6, so we can write:
A = 6x
B = 6y
Where x and y are positive integers.
Now, we are given that the LCM of A and B is 420. The relationship between the GCF and LCM is given by the formula:
LCM(A, B) = (A * B) / GCF(A, B)
Plugging in the values, we have:
420 = (6x * 6y) / 6
Simplifying further, we can cancel out the common factor of 6:
420 = 6xy
Now, one of the numbers is given as 60, which we can substitute into the equation:
420 = 6 * 60 * y
Simplifying further:
420 = 360y
Dividing both sides of the equation by 360:
y = 420 / 360
y = 7/6
As y should be a positive integer, the second number cannot be 7/6. Therefore, there seems to be an error in the given information or an inconsistency in the problem statement. Please verify the input and check for any mistakes.