In many of our previous post, we have already discuss about Prime number, Composite number, LCM and HCF. But before we solve this problem lets understand the meaning of Prime number, Composite number, LCM and HCF.
Because if we focus only on the solution of each question. we cannot understand the basics or the concept of the question. Once we grab or understand the original concept behind any mathematical question. we can solve that without seeing any solution.
So lets first understand the useful terms related to the question, What is the ratio of the LCM and HCF of the least composite number and the least prime number?
But before giving the solution of this problem. lets try to figure out the definition of some important terms related to this above question.
What is HCF and LCM in terms of Mathematics?
HCF is the Highest common factor of any natural number. If we define HCF in most simple words then it will be, HCF is a number which is a highest factor of two given numbers. HCF can only be calculated with two or more than two given numbers.
For example:- Lets take 30 and 90. Now, this two number has many number that can divide it completely. But those number which is greatest of them are known as HCF of 30 and 60.
Here, 1, 2, 3, 5, 10, 15, and 30 are the factor of 30 and 90. But 30 is the highest common factors known as HCF of 30 and 90.
Similarly, LCM stand for Lowest common multiple. LCM can be find of at least two or more than two numbers. Here, LCM can be define as The value or a natural number which is least common multiple of both the numbers.
For example:- Lets take 2, 4.
2 and 4 are two numbers which can divide 4, 8, 12 , ——— etc.
But by the definition of LCM, It is a least common multiple. So here 4 is the smallest number having 2 and 4 as divisor.
Please Note that :- Composite Number are those number which have more than two factors. for example, 4 is the smallest composite number.
Prime Number are those number which have only two factors. The interesting point is one factor of each number should be 1.
Now, After knowing all the terms related to this problem. It is now easy to answer this question as well as this types of another questions.
What is the ratio of the LCM and HCF of the least composite number and the least prime number?
- Least Composite Number :- As we have studied that a composite number are those number which have at least three factors. For example:- 4, 6, 8, 9, 10, ——– infinite.
Here, 4 is the smallest composite number. Because 4 has more than two factors.
Least Composite Number :- 4
- Least Prime Number:- As we have studied above that a prime number has only two factors having 1 and itself. For example:- 2, 3, 5, 7, 11, ——— infinite.
Here, 2 is the smallest prime number. Because 2 has only two factors 1 and itself.
Least Prime Number:- 2
Find the LCM and HCF of 4 and 2.
Prime Factorization of 4 and 2 is,
4 = 1, 2, and 4
2 = 1 and 2
Hence, the highest common factor of 4 and 2 is 2. So, HCF of 4 and 2 is 2.
Hence, the least common multiple of 4 and 2 is 4. So, LCM of 4 and 2 is 4.
Now,
We have to calculate the ratio of required LCM and HCF. So, the ratio is,
Ratio = (LCM of 4 and 2) / (HCF of 4 and 2)
Ratio = 4 / 2
Ratio = 2 / 1.
Hence, the ratio of LCM and HCF of least composite and least prime is 2/1.