Finding the Other Number Using HCF and LCM
This solution demonstrates how to find an unknown number when its Highest Common Factor (HCF), Least Common Multiple (LCM), and one of the numbers are provided. We utilize the fundamental relationship between these values.
Core Principle: Product Rule
The product of two numbers is always equal to the product of their HCF and LCM.
Let the two numbers be $N_1$ and $N_2$. The relationship is expressed as:
$ N_1 \times N_2 = \text{HCF} \times \text{LCM} $
Applying the Formula
We are given:
- HCF = 16
- LCM = 240
- One number ($N_1$) = 48
- We need to find the other number ($N_2$).
Substitute the known values into the formula:
$ 48 \times N_2 = 16 \times 240 $
Calculation
To find $N_2$, we isolate it:
$ N_2 = \frac{16 \times 240}{48} $
Simplify the calculation:
$ N_2 = \frac{16}{48} \times 240 $
Since $\frac{16}{48}$ simplifies to $\frac{1}{3}$:
$ N_2 = \frac{1}{3} \times 240 $
$ N_2 = 80 $
Thus, the other number is 80.
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.
- 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 HCF and the LCM of two numbers are 17 and 1224, respectively. If one of the numbers is 136, find the other one.
- 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?
