How to learn HCF and LCM | English

Some of you may have difficulties in understanding Highest Common Factor (HCF) and Least Common Multiple (LCM). But these mathematical concepts can be understood easily with some activities. Let's find out!

HCF: The numbers that can divide a given number completely (leaving a remainder of zero) are called its factors. The highest common factor (HCF) of a group of numbers is the largest common factor of the numbers. Lets find out how to find HCF of two numbers by some performing activities.

PRIME FACTORIZATION 0:59
One method of determining the HCF of two (or more) numbers is by representing both numbers as products of their prime factors. The HCF is a factor that is common to both/all numbers and also the largest such factor. Hence, we multiply all the prime factors that are common to both/all numbers in order to obtain the highest common factor of the two numbers.

CONTINUED DIVISION 3:02
Another method of determining the HCF of two numbers is by continued division. It is also called Euclid's Algorithm. It is a process by which we repeatedly eliminate the smaller number from the larger number until we get an equal number on both sides.

The steps to follow in continued division are as follows:
1. Make two columns and write one number in each column.
2. Compare the two numbers. Subtract the smaller number from the larger one.
3. Compare the two numbers again. Subtract the smaller number from the larger one.
4. Repeat this step until the numbers on both sides are equal. This number is the HCF of the two numbers we began the algorithm with.

Try both these methods with many different pairs/groups of numbers!
For smaller numbers, try to guess what the HCF/GCD would be and check your answer.
Use prime numbers with composite numbers or pairs/groups of prime numbers. What do you observe about their HCF in each case?

LCM 4:33
The smallest number which is a multiple of two numbers is called their least common multiple (LCM). The activity described in the video visually explains what the LCM of two numbers denotes - it is the smallest number where the multiples of the given pairs/groups of numbers coincide, i.e. the smallest number which is a multiple of all the numbers we are calculating the LCM of.

Make your own number line and cut out many strips of paper, divide each one of them into intervals representing different numbers, and try to find the LCMs of different pairs/groups of numbers!

Once again, what do you observe when you calculate the LCM of prime numbers, or prime and composite numbers, or composite numbers? Are the prime factors of each number in the pair/group also somehow related to their LCM?"

Presented by: Vrushali Sahasrabudhe, Sevasadan English Medium School, Pune

Produced by: IISER Pune Science Activity Center
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