Question

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

Answer 1

`L.C.M(14,6)=42`

Explanation:

There are two ways to find `" "L.C.M(14,6)`
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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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`" "0," "14," "28," "42.........`
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Multiples of 6 are :
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`" "0," "6," "12," "18," "24," "30," "36," "42........`
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Therefore, `" "L.C.M(14,6) = 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 :`" "color(blue)(9=3^2)" "and" "color(red)(6=2xx3)`
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`L.C.M(9,6) = color(blue)(3^2)xxcolor(red)2=18`
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Let us apply this method to find `" "L.C.M(14,6)`.
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`14=2xx7" " and " "6=2xx3`
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`L.C.M(14,6)=2xx3xx7=42`