The HCF and LCM of two numbers are 8 and 504 respectively.If one of the numbers is 56,find the smallest value of the other number
Given that the HCF (Highest Common Factor) of two numbers is 8 and the LCM (Least Common Multiple) is 504, and we know that one of the numbers is 56, we can find the other number.
First, we need to use the formula:
HCF * LCM = Product of the two numbers
So, we have:
8 * 504 = 56 * Other number
By simplifying this equation:
4032 = 56 * Other number
Now we can solve for the other number by dividing both sides of the equation by 56:
Other number = 4032 / 56
Other number = 72
Therefore, the smallest value of the other number is 72.
To find the smallest value of the other number, we need to use the relationship between HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers.
Given:
HCF of the two numbers = 8
LCM of the two numbers = 504
One of the numbers = 56
We can use the formula:
HCF × LCM = Product of the two numbers
Let's denote the other number as 'x'.
So, the equation becomes:
8 × 504 = 56 × x
To find the value of 'x', we can simplify the equation:
8 × 504 = 56 × x
4032 = 56 × x
Now, divide both sides of the equation by 56 to isolate 'x':
4032 ÷ 56 = x
72 = x
Therefore, the smallest value of the other number is 72.
8 = 2^3
56 = 2^3 * 7
504 = 2^3 * 3^2 * 7
That should get you started.