Question

Using prime factorization method find the hcf and lcm of 30 72 and 432 also show that hcf into lcm is not equal to product of three numbers

Answer 1

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Answer 2

$Given \: three \: numbers \: 30, 72 \: and \:432$

$We \:have , \\</p><p>30 = 2 \times 3 \times 5 ,\\</p><p>72 = 2 \times 2 \times 2 \times 3 \times 3= 2^{3} \times 3^{2}\\</p><p>432 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^{4} \times 3^{3}$

$HCF ( 30,72,432 ) = 2 \times 3 = 6$

/* ( Product of the smallest power of each common prime factors of the numbers )*/

$LCM ( 30,72, 432 ) = 2^{4}\times 3^{3}\times 5\\= 2160$

/* ( Product of the greatest power of each prime factors of the numbers ) */

$\red{ HCF \times LCM }\\ = 6 \times 2160 \\= 12960 \: --(1)$

$\red { Product \:of \: three \: numbers } \\= 30 \times 72 \times 432 \\= 933120 \: --(2)$

/* From (1) and (2) , we conclude that */

$LHS \red { \neq } \: RHS$

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