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Find the other number if the HCF of two numbers is 145, their LCM is 2175, and one of the numbers is 725.

Sagot :

GinnyAnsweridn
Certainly! Let's solve this step-by-step.

Given:
- The HCF (Highest Common Factor) of two numbers is 145.
- The LCM (Least Common Multiple) of the same two numbers is 2175.
- One of the numbers is 725.

We need to find the other number.

To do this, we'll use the relationship between HCF, LCM, and the two numbers:
[tex]\[ \text{HCF} \times \text{LCM} = \text{number1} \times \text{number2} \][/tex]

Given:
[tex]\[ \text{HCF} = 145 \][/tex]
[tex]\[ \text{LCM} = 2175 \][/tex]
[tex]\[ \text{number1} = 725 \][/tex]

Let's denote the unknown number as [tex]\(\text{number2}\)[/tex].

We can rearrange the formula to solve for [tex]\(\text{number2}\)[/tex]:
[tex]\[ \text{number2} = \frac{\text{HCF} \times \text{LCM}}{\text{number1}} \][/tex]

Now substitute the given values into the equation:
[tex]\[ \text{number2} = \frac{145 \times 2175}{725} \][/tex]

From calculation,
[tex]\[ \text{number2} = 435.0 \][/tex]

So, the other number is:
[tex]\[ \boxed{435} \][/tex]
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