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2 years ago

What is the least common multiple of 31, 28, and 14?

Mathematics

1 answer:

WINSTONCH [101]2 years ago

5 0

<u>⇨ By prime factorization method:</u>

$\begin{array}{r | l}{\sf{2 & {\sf14,28,31} \\\cline{2-2} {\sf2 & {\sf7,14,31 \\\cline{2-2} {\sf7 & {\sf7,7,31 \\\cline{2-2} {\sf31 & {\sf1,1,31 \\\cline{2-2} & {\sf1,1,1\end{array}$

${\sf{LCM\: = \:2 \:x\: 2 \:x\: 7 \:x\: 31}}\\\\{\sf{LCM \:= \:868}}\\}\\{\sf{Therefore,}}\\\\{\sf{LCM\:(14,\: 28,\: 31)\: = \:868$

${\boxed{\sf{LCM\:=\:868}}$

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The minimum initial velocity needed for the ball to clear the fence is $125.4\ \text{m/s}$

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