Question

find the HCF and LCM of 1152 and 1664 and verify the relationship between them

Answer 1

Heya !!




Prime factorisation of 1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3


Prime factorisation of 1664 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 13


HCF of 1152 and 1664 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128.



We know that,


One number × Other number = HCF × LCM


1152 ×1664 = 128 × LCM




LCM = ( 1152 × 1664/128 )


LCM = 14976.





Product of two numbers = 1152 × 1664 = 1916928.




LCM × HCF = 14976 × 128 = 1916928.




Hence,


Product of two Numbers = HCF × LCM

Answer 2

Prime factorization of 1,152 =>

1,152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

Prime factorization of 1,664 =>

1,664 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 13

LCM = 2^7 × 3^2 × 13 = 14,976

HCF = 2^7 = 128

LCM × HCF = A × B

=> 14,976 × 128 = 1,152 × 1,664

=> 19,16,928 = 19,16,928

Hence, verified.