Finding the Third Number
To find the third number when the highest common factor (HCF) of 3240, 3600, and this number is 36, and the least common multiple (LCM) is 2435520, follow these steps:
Step 1: Understanding HCF and LCM
The HCF of a set of numbers is the largest integer that divides each of them without leaving a remainder, while the LCM is the smallest integer that is a multiple of each of the numbers.
Step 2: Given Data
- HCF (3240, 3600, X) = 36
- LCM (3240, 3600, X) = 2435520
Step 3: Finding the Product of HCF and LCM
We can use the relation:
HCF(a, b, c) × LCM(a, b, c) = a × b × c
Substituting in the known values:
36 × 2435520 = 3240 × 3600 × X
‘Calculating the left side:
36 × 2435520 = 87619200
Step 4: Finding X
Now, we need to calculate:
87619200 = 3240 × 3600 × X
Finding the product of 3240 and 3600:
3240 × 3600 = 11664000
Thus, substituting in:
87619200 = 11664000 × X
Solving for X:
X = 87619200 ÷ 11664000
Calculating:
X = 7.5
However, since X must be an integer, we round it to the nearest integer, which gives us:
X = 8
Conclusion
The third number that satisfies the condition that the HCF is 36 and the LCM is 2435520 is 8.