# Find the LCM of $\sqrt{343}$.

Last updated date: 24th Mar 2023

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Answer

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Hint: Find the LCM of no. using prime factorization method. Break down the no. 343 as a multiple of prime no. Then take the root of the prime no.’s to get the LCM of $\sqrt{343}$.

Complete step-by-step answer:

LCM is the least common multiple; it is also referred to as the lowest common multiple.

For 2 integers a and b, denoted by LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example LCM(2,3)=6 and LCM(6,10)=30

We can take LCM by prime factorization method.

The method is to break down or express a given no. as a product of prime number. Where prime no. is a whole no. which is greater than 1, it is only divisible by 1 and itself.

$\therefore $LCM of $343=7\times 7\times 7$

where 7 is a prime no.

$\therefore \sqrt{343}=\sqrt{7\times 7\times 7}=7\sqrt{7}$

Note: LCM can be found by listing the factors, other than by prime factorization,

So, $343=7\times 7\times 7$

Complete step-by-step answer:

LCM is the least common multiple; it is also referred to as the lowest common multiple.

For 2 integers a and b, denoted by LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example LCM(2,3)=6 and LCM(6,10)=30

We can take LCM by prime factorization method.

The method is to break down or express a given no. as a product of prime number. Where prime no. is a whole no. which is greater than 1, it is only divisible by 1 and itself.

$\therefore $LCM of $343=7\times 7\times 7$

where 7 is a prime no.

$\therefore \sqrt{343}=\sqrt{7\times 7\times 7}=7\sqrt{7}$

Note: LCM can be found by listing the factors, other than by prime factorization,

So, $343=7\times 7\times 7$

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