Problem Analysis:
- We are given the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers.
- We are also given one of the numbers.
- The goal is to find the second number.
- Key terms: HCF, LCM, two numbers, find the other number.
Fundamental Number Property
There's a key relationship between two numbers and their HCF and LCM:
The product of two numbers is equal to the product of their HCF and LCM.
Mathematically, for two numbers $a$ and $b$: $a \times b = \text{HCF}(a, b) \times \text{LCM}(a, b)$
Identifying Given Values
Let the two numbers be $a$ and $b$. From the question:
- HCF = 17
- LCM = 1224
- Let $a = 136$
- We need to find $b$.
Calculating the Other Number
Using the property $a \times b = \text{HCF} \times \text{LCM}$:
$136 \times b = 17 \times 1224$
To find $b$, we rearrange the equation:
$b = \frac{17 \times 1224}{136}$Now, we simplify the calculation:
- Notice that $136$ is divisible by $17$. Specifically, $136 = 17 \times 8$.
- Substitute this into the equation: $b = \frac{17 \times 1224}{17 \times 8}$
- Cancel out the common factor $17$: $b = \frac{1224}{8}$
- Perform the division: $b = 153$
Therefore, the other number is 153.
Similar Questions
- The H.C.F. and the L.C.M. of two numbers are 5 and 495, respectively. If one of the numbers is 55, find the other one.
- The HCF of two numbers is 16 and their LCM is 240. If one number is 48, find the other number.
- 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?
- The LCM of two numbers is 721, and the numbers are in the ratio of 1 : 7. What is the sum of the numbers?
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:
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?
The sum of two numbers is 1215 and their HCF is 81. How many such pairs of numbers can be formed?
The LCM of two numbers in 48. Their ratio is 2:3 What is the sum of the numbers?
