Question

Find the hcf and lcm of 408 and 765 by fundamental theorem of arithmetic

Answer 1

Given that,

LCM and HCF of 408 and 765

We know that,

Fundamental theorem of arithmetic :

The arithmetic's fundamental theorem is defined by the factorization theorem.

The  factorization theorem shows that, any whole number greater than 1 can be show as the multiplication of prime numbers in only one way.

We know that,

LCM = least common multiple

HCF = highest common factor

We need to calculate the factor of 408 and 765

Using formula for factor

$408=2\times2\times2\times3\times17$

$765 =3\times3\times5\times17$

We need to calculate the LCM of 408 and 765

Using factors

$\text{LCM of 408 and 765}=2\times2\times2\times3\times3\times5\times17$

$\text{LCM of 408 and 765}=6120$

We need to calculate the HCF of 408 and 765

Using factors

$\text{HCF of 408 and 765}=3\times17$

$\text{HCF of 408 and 765}=51$

Hence, HCF and LCM of 408 and 765 are 51 and 6120.

Answer 2

Given:

Numbers : 408 and 765

To Find :

Find the hcf and lcm

Solution:

Numbers : 408 and 765

HCF :

2 | 408                 3 | 765

2 | 204                 3 | 255

2 | 102                  5 |  85

3 |  51                    17 | 17

17 |  17                        | 1

   |  1

$408 = 2 \times 2 \times 2 \times 3 \times 17 \\765 = 3 \times 3 \times 5 \times 17 \\HCF = 3 \times 17 =51$

LCM :

2 | 408,765

2 | 204,765

2 | 102 , 765

3 |  51,765

3 | 27 , 255

3 | 9 , 85

3 | 3 ,85

5 | 1 , 85

17 | 1 , 17

   |  1 ,1

$LCM = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5 \times 17=55080$

Hence The HCF and LCM are 51 and 55080