Question

Q4. Using prime factorization, find the HCF and LCM of 72, 126 and 168. Also show that HCF x LCM ≠ product of the three numbers.

Answer 1

Hey.

Here is the answer.

72 = 2×2×2×3×3

126 = 2×3×3×7

168=2×2×2×3×7

So, HCF = 2×3 =6

LCM = 2×2×2×3×3×7 = 504

To show : HCF× LCM ≠ product of 3 nos.

HCF× LCM =( 2×3)×(2×2×2×3×3×7)

= 2^4 × 3^3 ×7

product of nos. = (2×2×2×3×3)×(2×3×3×7)×(2×2×2×3×7)

= 2^7 × 3^5 × 7^2

Hence, LHS ≠ RHS.

Thanks.

Answer 2

Heya !!!

Prime factorisation of 72 = 2 × 2 × 2 × 3 × 3

Prime factorisation of 126 = 2 × 3 × 3 × 7

Prime factorisation of 168 = 2 × 2 × 2 × 3 × 7

HCF of 72 , 168 and 126 = 2 × 3 × = 6

And,

LCM of 72 , 126 and 168 = 2 × 2 × 2 × 3× 3 × 7 = 504

Product of three numbers = 72 × 126 × 168 = 1524096

Product of LCM and HCF = 504 × 6 = 3024.

Hence,

Product of three Numbers is not equal to their product of HCF and lCM.

HOPE IT WILL HELP YOU.... :-)