Question

find the lcm and hcf of 408 and 170 by applying the fundamental theorem of arithmetic​

Answer 1

Hi there !

Fundamental theorem of arithmetic :

Fundamental theorem of arithmetic :Every composite number can be expressed as a product of primes, and this factorisation is unique except for the order in which the prime factors occur.

Finding LCM and HCF by factorisation method .

408 = 2³×17×3

170=2×5×17

L.C.M (highest power)= 2³×5×3×17= 2040

H.C.F (lowest power) =17×2=34

Thankyou :)

Answer 2

$HCF(408,170)=34$

$LCM(408,170)=2040$

Step-by-step explanation:

To find : The LCM and HCF of 408 and 170 by applying the fundamental theorem of arithmetic​ ?

Solution :

Fundamental theorem of arithmetic states that,

Every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes

So factor the numbers,

$408 = 2\times 2\times 2\times 3\times 17$

$170=2\times 5\times 17$

HCF is the highest common factor,

$HCF(408,170)=2\times 17$

$HCF(408,170)=34$

LCM is the least common factor,

$LCM(408,170)=2\times 2\times 2\times3\times 5\times 17$

$LCM(408,170)=2040$

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