MathematicsFind the HCF and LCM of 6, 72 and 120 using the fundamental theorem of arithmetic.

Find the HCF and LCM of 6, 72 and 120 using the fundamental theorem of arithmetic.

A
HCF = 6 and LCM = 360
B
HCF = 5 and LCM = 120
C
HCF = 3 and LCM = 360
D
HCF = 6 and LCM = 240

Solution:

Given are three numbers 6, 72 and 120.
The prime factorization of

6, 72

and

120

is,

⇒ 6 = 2 × 3 ⇒ 72 = 2 × 2 × 2 × 3 × 3 ⇒ 72 = 23 × 32

And,

⇒ 120 = 2 × 2 × 2 × 3 × 5 ⇒ 120 = 23 × 3 × 5

So, the HCF of 6, 72 and 120 is,

⇒ H C F = 21 × 31 ⇒ H C F = 2 × 3 ⇒ H C F = 6

Hence the HCF of 6, 72 and 120 is 6.
Now, the LCM of 6, 72 and 120 is,

⇒ L C M = 23 × 32 × 51 ⇒ L C M = 8 × 9 × 5 ⇒ L C M = 360

Hence the HCF and LCM are 6 and 360 respectively.
Therefore the correct answer is option (1).