The HCF and lcm of 12 15 21 respectively are :

lcm of 12, 15 21 by prime factorization **method **

lcm of 12, 15, and 21 by prime factorization

In this problem, we will find the LCM and HCF of 12 15, and 21 by the prime factorizing method. So, now we are doing the factors of the given numbers.

We will use the following concepts:

HCF = a number that divides all numbers.

LCM = A common number that could be completely divisible by all three given numbers.

## Find The LCM And HCF of 12 15 And 21

So, first of all, we will do the factors of these given numbers 12, 15, and 21

By seeing the numbers we can identify that all these are common numbers. Now we will factorize them into prime numbers. Prime numbers can’t be divided further.

Hence the factors of 12 are as follow:

12 = 2X2X3

Hence the factors of 15 are as follow:

15 = 3X5

Hence the factors of 21 are as follow:

21 = 3X7

Let’s see all together

12 = 2X2X3

15 = 3X5

21 = 3X7

Here we can see common factor is only 3 because all numbers can be divide by 3.

So, the HCF or Highest Common Factor = 3

LCM = 2X2X3X5X7

LCM = 420.

Here we find the all numbers 12, 15, and 21 has common HCF is 3.

Now we will verify the relationship for calculating that our answer is correct on not.

SO, for verifying our we will use standard relationship

**LCM _{(a,b,c)} = ( multiplication of numbers X HCF )/ {(HCF of a, b)(HCF of b, c)(HCF of c, d)}**

where a, b, c are the three numbers

LCM_{(a, b, c)} = 420

HCF_{(a, b, c)} = 3

aXbXc = 12X15X21 = 3780

HCF_{(a, b)} = 3

HCF_{(b, c)} = 3

HCF_{(c, a)} = 3

Now we will put all the values in the standard relationship

**LCM _{(a,b,c)} = ( multiplication of numbers X HCF )/ {(HCF of a, b)(HCF of b, c)(HCF of c, d)}**420 = (3780*3) / (3*3*3)

420 = (3780*3) / (3*3*3)

420 = 3780/9

420 = 420

### Find The LCM And HCF of 12 15 And 21 By Factorization Method

Let’s take this example from the classroom whiteboard.

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