The LCM of the numbers is 1200. Which of the following cannot be their HCF? a) 600 b) 400 c) 500 d) 200
Hint: The least number which is exactly divisible by each of the given numbers is called the least common multiple and the largest number that divides two or more numbers is the highest common factor (HCF). By using this definition, we calculate the required thing.
Complete step-by-step answer: Factors and Multiples: All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. Multiples are those numbers which we get after multiplying numbers. To find the LCM of the given numbers, we express each number as a product of prime numbers. The product with the highest power of the prime numbers that appear in prime factorization of any of the numbers gives us the LCM. To find the HCF of the given numbers, we express each number as a product of prime numbers. The highest prime factor is HCF. Now, proceeding to our question, let the two numbers be x and y. From the details given in question, The four options given in question are 600, 400, 500, and 200. Considering all the options individually, 500 cannot be the HCF of two numbers whose LCM is 1200 since it cannot divide 1200 completely without leaving remainder. Hence, 500 cannot be the HCF. Therefore, option (c) is correct.
Note: The key step in solving this problem is the basic definition of LCM and HCF. So, by using the definition we obtained our answer. This knowledge is useful in solving complex problems of mathematics.