Question

find the HCF and LCM of 29029 and 1740 by using the fundamental theorem of arithmetic

Answer 1

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Answer 2

Answer:

HCF(29029,1740)=29

LCM(29029,1740)=1741740

Step-by-step explanation:

Given : Numbers 29029 and 1740

To find : The HCF and LCM of 29029 and 1740 by using the fundamental theorem of arithmetic.

Solution : Using the fundamental theorem of arithmetic is represented as product of prime factors

First we find the prime factors of 29029 and 1740

$290297= 7\times 11 \times 13 \times 29$

$1740=2 \times 2 \times 3 \times 5 \times 29$

HCF is the highest common factor of 29029 and 1740 is 29

HCF(29029,1740)=29

We know, Product of two numbers = HCF × LCM

Product of two numbers = $29029\times1740= 50510460$

Product of two numbers = HCF × LCM

$50510460=29\times LCM$

$LCM=\frac{50510460}{29}$

$LCM=1741740$

Therefore, LCM(29029,1740)=1741740