Find the HCF and LCM of 12 72 and 120 by The Prime Factorization Method

In this problem, we will find the HCF and LCM of 12 72 and 120 by The Prime Factorization Method. So, now we are doing the factors of the given numbers.

We will use the following concepts:
HCF = Greatest or highest number that divides all numbers.
LCM = A common smallest number that could be completely divisible by all three given numbers.

Find The LCM And HCF of 12 72 And 120

So, first of all we will do the factors of these given numbers 12, 72, and 120

By seeing the numbers we can identify that all these are general 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 72 are as follow:
72 = 2X2X2X3X3

Hence the factors of 120 are as follow:
120 = 2X2X2X3X5

Let’s see all together
12 = 2X2X3
72 = 2X2X2X3X3
120 = 2X2X2X3X5

Here we can see common factors are 2X2X3. This is equal to 12.

So, the HCF or Highest Common Factor = 12
Because all numbers can be divide by 12.

HCF = 12

LCM or Least Common Multiply of 12, 72, and 120

LCM = 2X2X2X3X3X5
LCM = 360.

Here we find that the HCF of all numbers 12, 72, and 120 is 12.
Here we find that the LCM of all numbers 12, 72, and 120 is 360.

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 12, 72, and 120 respectivly.

LCM_{(a, b, c)} = 360
HCF_{(a, b, c)} = 12
aXbXc = 12X72X120 = 103680
HCF_{(a, b)} = 2X2X3 = 12
HCF_{(b, c)} = 2X2X2X3 = 24
HCF_{(c, a)} = 2X2X3 = 12

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)}

360 = (103680*12) / (12*24*12)
360 = (103680) / (12*24)
360 = (103680) / (12*24)
360 = 4320/12
360 = 360