Ratio Numbers LCM Calculation
Let the two numbers be represented based on their given ratio of 1:7. We can express these numbers as $k$ and $7k$, where $k$ is a common factor.
LCM Relationship Explained
The Least Common Multiple (LCM) of two numbers $a$ and $b$ is the smallest positive integer that is divisible by both $a$ and $b$. For numbers $k$ and $7k$, their LCM is $7k$. This is because $7k$ is divisible by $k$ (result is 7) and by $7k$ (result is 1).
Calculating the Common Factor
We are given that the LCM of the two numbers is 721. Using the relationship derived above:
$7k = 721$
To find the value of $k$, we divide both sides of the equation by 7:
$k = \frac{721}{7}$
$k = 103$
Determining the Numbers
Now that we have the value of $k$, we can find the two numbers:
- First number: $k = 103$
- Second number: $7k = 7 \times 103 = 721$
Sum of Numbers Calculation
The question asks for the sum of these two numbers. We add the numbers found:
Sum = $103 + 721$
Sum = $824$
Thus, the sum of the two numbers is 824.
Similar Questions
- If the LCM of $20x^3y^2$ and $10x^4y^4$ is $20x^4y^4$, find the HCF.
- There are four table clocks. They ring every 10 min, 15 min, 20 min and 25 min respectively. If they all ring together at 10 a.m., then at what time will they ring together again?
- Find the HCF of $12 \times 15, 15 \times 21, 21 \times 12$
- How many numbers less than 10000 are there which are exactly divisible by 21, 35 and 63?
- A, B and C begin together to move around a circular stadium and they complete their revolutions in 42 s, 63 s and 84 s respectively. After how much time will they come together at the starting point?
What is the LCM of $\sqrt[2]{169}$, $\sqrt[3]{27}$, $\sqrt[3]{64}$ and $\sqrt[2]{144}$ ?
- The HCF of $28\ p^5q^2$ and $70\ p^3q^4$ is:
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- What is the greatest number which divides 13, 26 and 39 and gives the remainders as 1, 2 and 3 respectively?
- The LCM of x and y is 2079 and their HCF is 27. If x = 189, what will be the value of y?
Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
