LCM, HCF, GCD: Basic concept, calculation, applications explained
LCM, HCF, GCD: Basic concept, calculation, applications explained
Introduction
Concept of LCM, HCF important for number theory and remainder based problems (generally asked in SSC CGL, CAT.)
LCM is important for time and speed, time and work problems.
LCM is also important for circular racetracks, bells, blinking lights, etc.
HCF is important for largest size of tiles, largest size of tape to measure a land etc.
But before getting into LCM, HCF, let’s understand
What is Prime number?
Consider this number : 12. This number can be found in many multiplication tables for example
1 x 12=12.
2 x 6 =12
3 x 4=12
That means, 12 has many factors (1,2,3,4,6,12). Such number is called a composite number.
On the other hand, consider this number: 29. You cannot find it in any table except 29 x 1 =29. Such number is called a prime number.
Let’s make a shortlist from exam point of view
Prime Non-prime (composite)
2,3,5,7,11,13,17,19,23,29 4,6,8,9,10,12,14,15….
Now hold this prime number thought in your mind for a while.
What is LCM?
First, let’s create multiplication tables of 4 and 6.
4′s table multiple 6′s table multiple
4 x 1 = 4 6 x 1 = 6
4 x 2 = 8 6 x 2 = 12
4 x 3 = 12 6 x 3 = 18
4 x 4 = 16 6 x 4 = 24
4 x 5 = 20 6 x 5 = 30
4 x 6 = 24 6 x 6 = 36
4 x 7 = 28 6 x 7 = 42
4 x 8 = 32 6 x 8 = 48
4 x 9 = 36 6 x 9 = 54
Do you see any common numbers in the multiples of 4 and 6?
Yes I see 12, 24 and 36 are common in both tables. Let’s isolate them.
4 x 3 = 12 6 x 2 = 12
4 x 6 = 24 6 x 4 = 24
4 x 9 = 36 6 x 6 = 36
Ok so 12, 24 and 36 are common multiples of 4 and 6. But what is the smallest of these multiples? Ans 12 is smallest.
In the exam, we’ve no time to make such ^big tables to find LCM. So how to quickly find LCM of two or three numbers? There are many tricks, the easiest one is prime-factorization. We’ll learn that in a bit, but before that:
LCM4 EXam
Suppose there is a circular race track. Tarak Mehta takes 4 minutes to finish it
Introduction
Concept of LCM, HCF important for number theory and remainder based problems (generally asked in SSC CGL, CAT.)
LCM is important for time and speed, time and work problems.
LCM is also important for circular racetracks, bells, blinking lights, etc.
HCF is important for largest size of tiles, largest size of tape to measure a land etc.
But before getting into LCM, HCF, let’s understand
What is Prime number?
Consider this number : 12. This number can be found in many multiplication tables for example
1 x 12=12.
2 x 6 =12
3 x 4=12
That means, 12 has many factors (1,2,3,4,6,12). Such number is called a composite number.
On the other hand, consider this number: 29. You cannot find it in any table except 29 x 1 =29. Such number is called a prime number.
Let’s make a shortlist from exam point of view
Prime Non-prime (composite)
2,3,5,7,11,13,17,19,23,29 4,6,8,9,10,12,14,15….
Now hold this prime number thought in your mind for a while.
What is LCM?
First, let’s create multiplication tables of 4 and 6.
4′s table multiple 6′s table multiple
4 x 1 = 4 6 x 1 = 6
4 x 2 = 8 6 x 2 = 12
4 x 3 = 12 6 x 3 = 18
4 x 4 = 16 6 x 4 = 24
4 x 5 = 20 6 x 5 = 30
4 x 6 = 24 6 x 6 = 36
4 x 7 = 28 6 x 7 = 42
4 x 8 = 32 6 x 8 = 48
4 x 9 = 36 6 x 9 = 54
Do you see any common numbers in the multiples of 4 and 6?
Yes I see 12, 24 and 36 are common in both tables. Let’s isolate them.
4 x 3 = 12 6 x 2 = 12
4 x 6 = 24 6 x 4 = 24
4 x 9 = 36 6 x 6 = 36
Ok so 12, 24 and 36 are common multiples of 4 and 6. But what is the smallest of these multiples? Ans 12 is smallest.
In the exam, we’ve no time to make such ^big tables to find LCM. So how to quickly find LCM of two or three numbers? There are many tricks, the easiest one is prime-factorization. We’ll learn that in a bit, but before that:
LCM4 EXam
Suppose there is a circular race track. Tarak Mehta takes 4 minutes to finish it