Question

Find the HCF and LCM of 11008 and 7344 using fundamental theorem of arithmetic​

Answer 1

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11008 = 2⁸ × 43

7344 = 2⁴ × 7²

HCF = 2⁴ = 16

LCM = 2⁸ × 7² × 43 = 539392

Answer 2

$\bf \: HCF(11008,7344) = 16$

$\bf \: LCM(11008,7344) = 5052672$

Given:

• Two numbers 11008 and 7344.

To find:

• Find the HCF and LCM of given numbers using fundamental theorem of arithmetic.

Solution:

Concept/Formula to be used:

Fundamental theorem of arithmetic: It states that, Every integer, greater than one can be represented uniquely as a product of prime numbers/factors

It is also called unique factorization theorem and prime factorization theorem.

Step 1:

Write the prime factors of both numbers.

$11008 = {2}^{8} \times 43$

$7344 = {2}^{4} \times {3}^{3} \times 17$

Step 2:

Find HCF and LCM of numbers.

$HCF(11008,7344) = {2}^{4}$

$\bf \: HCF(11008,7344) = 16$

and

$LCM(11008,7344) = {2}^{8} \times {3}^{3} \times 17 \times 43$

$LCM(11008,7344) = 256 \times 27 \times 17 \times 43$

$\bf \: LCM(11008,7344) = 50,52,672$

Thus,

The LCM and HCF of the numbers are 50,52,672 and 16 respectively.

Learn more:

1) Find the LCM of 15, 30, 60, 90

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2) 4. Find the HCF of 30, 42, and 96 prime factorization method.

https://brainly.in/question/22060389

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