Finding the Other Number Using HCF and LCM
We are given the Highest Common Factor (HCF), the Least Common Multiple (LCM), and one of the two positive integers. We need to find the second integer.
Key Formula: For any two positive integers, let's say \(a\) and \(b\), the product of the integers is equal to the product of their HCF and LCM.
\( a \times b = HCF(a, b) \times LCM(a, b) \)
Applying the Formula
Let the two positive integers be \(a\) and \(b\). We are given:
- HCF = 12
- LCM = 924
- One number, let's say \(a = 84\)
- We need to find the other number, \(b\).
Calculation Steps
Substitute the known values into the formula:
\( 84 \times b = 12 \times 924 \)
Now, solve for \(b\):
\( b = \frac{12 \times 924}{84} \)
First, calculate the product of HCF and LCM:
\( 12 \times 924 = 11088 \)
Now, divide this product by the known number (84):
\( b = \frac{11088}{84} \)
Performing the division:
\( b = 132 \)
Therefore, the other number is 132.
Similar Questions
- Three bells ring at intervals of 15, 30 and 45 minutes respectively. At what time will they ring together again, if they rang simultaneously at 8.00 AM?
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
