Question

Using prime factorization method find the hcf and lcm of 72 126 and 168

Answer 1

72 = 2*2*2*3*3 = 2³*3²
126 = 2*3*3*7 = 2*3²*7
168 = 2*2*2*3*7 = 2³*3*7

HCF = 2 *3 = 6
LCM = 2³ *3² = 216


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Answer 2

Answer:

The HCF(72,126, 168)= 6

The LCM(72,126, 168)=504

Step-by-step explanation:

Given : Numbers - 72,126 and 168

To find : The HCF and LCM of 72,126 and 168

Solution :

Using Fundamental theorem of arithmetic which state that every integer greater than 1 is prime number or presented as product of prime factorization.

Now, factor of number 72,126 and 168

$72 = 2\times2\times2\times3\times3 = 2^3\times3^2$

$126 = 2\times3\times3\times7 = 2\times3^2\times7$

$168 = 2\times2\times2\times3\times7 = 2^3\times3\times7$

HCF is the highest common factor

$HCF(72,126, 168) = 2\times3=6$

LCM is the least common multiple  

So, the common number with highest power

$LCM(72,126, 168) = 2^3\times3^2\times7^1=504$

Therefore,

The HCF(72,126, 168)= 6

The LCM(72,126, 168)=504