Question #738f7

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Question #738f7

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Answer 1 · 2017-12-06T11:36:17

$24 minutes$ $24 " minutes"$

Explanation:

$lcm (6, 8) = 24$ $lcm(6,8) = 24$
(least common multiple)
$lcm (a, b) = \frac{a \cdot b}{gcd (a, b)}$ $lcm(a,b) = (a*b)/gcd(a,b)$
$\Rightarrow lcm (8, 6) = \frac{8 \cdot 6}{gcd (8, 6)}$ $=> lcm(8,6) = (8*6)/gcd(8,6)$
$and gcd (8, 6) = gcd (6, 2) = 2$ $and gcd(8,6) = gcd(6,2) = 2$
$"because" gcd(a,b) = gcd(a-b, b) if a > b$
(greatest common divisor)
$=> lcm(8,6) = 48/2 = 24$

Answer 2 · 2017-12-06T11:43:44

We need to calculate LCM of the two given timings: $6and8$ min.

factors of $6->ul2xx3$
factors of $8->ul2xx2xx2$
LCM $=2xx3xx2xx2$ ( $ul2$ is included once)
LCM $=24$ min

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Question #738f7

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