Question

four men can walk 105,112,126,168 kilometres in a week respectively then the least distance they can walk in an exact number of week is

(a) 5040 km
(b) 1680 km
(c) 630 km
(d) none​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Four men can walk 105,112,126,168 kilometres in a week respectively then the least distance they can walk in an exact number of week is

(a) 5040 km

(b) 1680 km

(c) 630 km

(d) none

EVALUATION

Here it is given that four men can walk 105,112,126,168 kilometres in a week respectively

Now in order to find the least distance they can walk in an exact number of week we have to find the LCM of 105,112,126,168

Now

105 = 3 × 5 × 7

112 = 2 × 2 × 2 × 2 × 7

126 = 2 × 3 × 3 × 7

168 = 2 × 2 × 2 × 3 × 7

∴ LCM

= 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7

= 5040

Hence the least distance they can walk in an exact number of week = 5040 kilometer

FINAL ANSWER

Hence the correct option is (a) 5040 km

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Answer 2

$\Large{\underbrace{\underline{\sf{Understanding\; the\; Question}}}}$

Here in this question, concept of LCM(lowest common multiple) is used. We are given that 4 men can walk 105,112,126 and 168 kilometres respectively in a week and we are asked to find the least distance they should travel in exact no. Of weeks. To find the required distance we have to find the LCM of the distance covered by them in one week.

So let's do it!!

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~Prime factorisation

105=5×7×3

112=2×2×2×2×7=2⁴×7

126=2×3×3×7=2×3²×7

168=2×2×2×7×3=2³×7×3

So their LCM=5×7×3²×2⁴=5040

It means that 4 men should travel 5040km in exact number of weeks.

Required answer is 5040km.

Option (a) is correct.

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