The sum of the HCF and LCM of two numbers is 680 and the LCM is 84 times of the HCF.lf one number is 56 ,find the other.
Let the other number be x.
Given that the LCM of 56 and x is 84 times their HCF, we have:
LCM (56, x) = 84 * HCF (56, x)
We know that HCF (56, x) = 56 (since 56 is a factor of both numbers)
Now, using the property:
LCM (a, b) * HCF (a, b) = a * b
We can rewrite the equation as:
84 * 56 = 56 * x
Simplifying, we get:
4704 = 56x
Dividing both sides by 56, we get:
x = 4704 / 56
x = 84
Therefore, the other number is 84.
Let's solve this step by step.
Step 1: Let's assume the other number as 'x'.
Step 2: We are given that the HCF (Highest Common Factor) + LCM (Least Common Multiple) of the two numbers is 680. Therefore, we can write the equation as:
HCF + LCM = 680
Step 3: We are also given that the LCM is 84 times the HCF. Therefore, we can write another equation as:
LCM = 84 * HCF
Step 4: Now, using the fact that LCM = (Number 1 * Number 2) / HCF, we can substitute LCM in the first equation, we get:
HCF + (Number 1 * Number 2) / HCF = 680
Substituting the values Number 1 = 56 and HCF = 56:
56 + (56 * x) / 56 = 680
Simplifying:
56 + x = 680
Step 5: Now, let's solve for 'x' by subtracting 56 from both sides of the equation:
x = 680 - 56
x = 624
Therefore, the other number is 624.