On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm, and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?
We have to find LCM of 40, 42 and 45 to get the required minimum distance.
For this we find prime factorisations.
40 = 2 × 2 × 2 × 5.
42 = 2 × 3 × 7
45 = 3 × 3 × 5
LCM (40, 42, 45) = 2 × 3 × 5 × 2 × 2 × 3 × 7 = 2520
Hence, Minimum distance each should walk 2520 cm. So that each can cover the same distance in complete steps.
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in the form 2m × 5n, where m, n are non-negative integers. Hence, write its decimal expansion, without actual division.