# How do you find the Least common multiple of 14, 6?

Dec 2, 2016

$L . C . M \left(14 , 6\right) = 42$

#### Explanation:

There are two ways to find $\text{ } L . C . M \left(14 , 6\right)$
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First method:
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List the multiples of 14 .
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List the multiples of 6.
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Choose the non-zero common multiple between the two lists.
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Let us apply it:
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Multiples of 14 are:
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$\text{ "0," "14," "28," } 42. \ldots \ldots . .$
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Multiples of 6 are :
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$\text{ "0," "6," "12," "18," "24," "30," "36," } 42. \ldots \ldots .$
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Therefore, $\text{ } L . C . M \left(14 , 6\right) = 42$
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Second method:
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Write the prime factorization of 14 and 6.
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Take all the prime numbers with highest exponent from the prime factorization.
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Ex :$\text{ "color(blue)(9=3^2)" "and" } \textcolor{red}{6 = 2 \times 3}$
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$L . C . M \left(9 , 6\right) = \textcolor{b l u e}{{3}^{2}} \times \textcolor{red}{2} = 18$
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Let us apply this method to find $\text{ } L . C . M \left(14 , 6\right)$.
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$14 = 2 \times 7 \text{ " and " } 6 = 2 \times 3$
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$L . C . M \left(14 , 6\right) = 2 \times 3 \times 7 = 42$