Question
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.
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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.
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.
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