How to crack LCM & HCF questions

LCM (Lowest common multiple) & HCF (Highest common factor) are important and part of the Number System. One should understand it to solve important number theory based questions and remainder theorem as well. Knowledge of LCM and HCF comes in handy when you will solve questions on Time and work.

We have already understood Number System briefly in our previously published article: Learn Number System in Quantitative Aptitude

Now let us understand LCM & HCF more in detail:

The Lowest Common Multiple (L.C.M) is the smallest number that is a common multiple of two or more numbers. The simplest method to find out LCM is prime factorization method. The simple method of finding the L.C.M of smaller numbers is to write down the multiples of the larger number until one of them is also a multiple of the smaller number.

If a natural number is expressed as the product of prime numbers, then the factorisation of the number is called its prime (or complete) factorisation.

Example:

Find the Lowest Common Multiple of 8 and 12.

Solution: Multiples of 12 are 12, 24...

              24 is also a multiple of 8, so the L.C.M of 8 and 12 is 24.

The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers. In other words the H.C.F is the largest of all the common factors. HCF is usually useful in simplifying fractions.

Example:

The common factors or of 12 and 18 are 1, 2, 3 and 6. 

The largest common factor is 6, so this is the H.C.F. of 12 and 18.

What is a Common Factor?

When two (or more) numbers have the same factor, that factor is called a common factor.

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