The HCF and LCM of two numbers are 8 and 504 respectively one of the numbers is 72 . determine the other number.
HCF*LCM = 8*504 = 4032
one of the numbers is 72, the other must be 4032/72 = 56
check:
72 = 2*2*2*3*3
56 = 2*2*2*7
HCF = 2*2*2 = 8
LCM = 2*2*2*3*3*7 = 504
To find the other number, we need to use the relationship between the highest common factor (HCF) and the least common multiple (LCM) of two numbers.
Let's denote the two numbers as x and y. We know that the HCF of x and y is 8, and the LCM of x and y is 504.
We can use the formula:
LCM(x, y) = (x * y) / HCF(x, y)
Plugging in the given values, we have:
504 = (x * 72) / 8
To solve for x, we can cross-multiply:
504 * 8 = x * 72
Simplifying further:
4032 = 72x
Dividing both sides by 72:
4032 / 72 = x
x = 56
So, the other number is 56.
To find the other number, we need to use the relationship between the highest common factor (HCF) and the least common multiple (LCM).
The HCF of two numbers represents the largest common factor/divisor between those two numbers.
The LCM of two numbers represents the smallest multiple that is divisible by both of those numbers.
Given:
HCF = 8
LCM = 504
One of the numbers = 72
To solve for the other number, we can use the formula:
LCM = (Number 1 * Number 2) / HCF
Substituting the given values:
504 = (72 * Number 2) / 8
To remove the fraction, we can cross-multiply:
504 * 8 = 72 * Number 2
Simplifying both sides:
4032 = 72 * Number 2
Now, divide both sides by 72 to solve for Number 2:
4032 / 72 = Number 2
Number 2 = 56
Therefore, the other number is 56.