HCF AND LCM

 

     HCF AND LCM chapter is very useful for nmms exam, Dsc, Aptet, Tstet, rrb, ssc, and bank po's exams. Find hcf and lcm multiple choice questions quiz is very useful for all competitive aspirants

Highest Common Factor:

                Definition: - The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common Divisor. (GCD).

 The HCF of 20, 28 and 36 can also be found by prime factorization of these numbers as follows:

Thus, 20 = 2×2×5

           28= 2×2×7

           36= 2×2×3×3

The common factor of 20, 28 and 36 is 2 (occurring twice). Thus, HCF of 20, 28 and 36 is 2×2=4.

Lowest Common Multiple:

Definition: - The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least of their common multiples.

What will be the LCM of 12 and 18

Solutions: - The prime factorisations of 12 and 18 are

12= 2×2×3;                        18= 2×3×3

In these prime factorisations, the maximum number of times the prime factor 2 occurs is two; this happens for 12. Similarly, the maximum number of times the factor 3 occurs is two; this happens for 18. The LCM of the two numbers is the product of the prime factors counted the maximum number of times they occur in any of the numbers. Thus, in this case LCM = 2×2×3×3= 36.

  Find the LCM of 20, 25 and 30

 

So, LCM = 2×2×3×5×5