Question

Find the lcm of 290, 360,480

Answer 1

The instructions to find the LCM of 290, 360 and 480 are the next:-

1)Decomposing All Numbers into Prime Factors:-

$290 |2 | \\145 |5| \\ 29 |29| \\ 1 |0|$

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$360 |2| \\ 180 |2| \\ 90|2| \\ 45 |3| \\ 15 |3| \\5 |5| \\ 1 |0|$

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$480 |2| \\ 240 |2| \\ 120 |2| \\ 60 |2| \\ 30 |2| \\ 15 |3| \\ 5 |5| \\ 1 |0|$

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2)Write All Numbers As The Product Of It's Prime Factors:-

$prime \: \: factors \: \: of \: \: 290 = 2 \: . \: 5 \: . \: 29 \\ prime \: \: factors \: \: of \: \: 360 = 2 {}^{2}. \: \: 3 {}^{2} . \: \: 5 \\ prime \: \: factors \: \: of \: \: 480 = 2 {}^{5} . \: \: 3 \: \: . \: \: 5$

3)Choose the common and Uncommon Prime Factors with the Greatest Exponent:-

$common \: \: prime \: \: factors = 2 \: \: and \: \: 5 \\ common \: \: prime \: \: factors \: \: with \: \: the \: \: greatest \: \: exponent = 2 {}^{5} and \: \: 5 {}^{1} \\ uncommon \: \:prime \: \: factors \: \: = 29 \: \: and \: \: 3 \\ uncommon \: \: prime \: \: factors \: \: with \: \: the \: \: greatest \: \: exponent = 29 {}^{1} and \: \: 3 {}^{2}$

4)Caluculate the Least Common Multiple Or LCM:-

$remember \: \: to \: \: find \: \: the \: \: lcm \: \: of \: \: several \: \: numbers \: \: you \: \: must \: \: multiply \: \: the \: \: common \: \: and \: \: uncommon \: \: prime \: \: factors \: \: with \: \: the \: \: greatest \: \: exponent \: \: of \: \: those \: \: numbers. \\ \\ lcm = 2 {}^{5} . \: 5 {}^{1} . \: 29 {}^{1} . \: 3 {}^{2} = 41760$

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