Three delivery workers are unloading boxes at a warehouse. Each of them takes steps of different lengths: 48 cm, 54 cm, and 60 cm respectively. They all start from the same point and walk along a straight path.

Consider the following statements:
Statement I: The minimum distance at which all three workers will step on the same spot again is 21 meters and 60 centimetres.
Statement II: The LCM of their step lengths is 2520 cm.

Select the correct answer from the options below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

Three delivery workers are unloading boxes at a warehouse. Each of them takes steps of different lengths: 48 cm, 54 cm, and 60 cm respectively. They all start from the same point and walk along a straight path.

Consider the following statements:
Statement I: The minimum distance at which all three workers will step on the same spot again is 21 meters and 60 centimetres.
Statement II: The LCM of their step lengths is 2520 cm.

Select the correct answer from the options below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

LCM of 48, 54, and 60:
48 = 2⁴ &times; 3
54 = 2 &times; 3&sup3;
60 = 2&sup2; &times; 3 &times; 5
LCM = 2⁴ &times; 3&sup3; &times; 5 = 16 &times; 27 &times; 5 = 2160 cm = 21 meters 60 centimetre.
Statement I is correct.
Statement II is incorrect (2520 is not the correct LCM).
Hence, option a is correct.

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E Question 1	⏱ 0
Three delivery workers are unloading boxes at a warehouse. Each of them takes steps of different lengths: 48 cm, 54 cm, and 60 cm respectively. They all start from the same point and walk along a straight path. Consider the following statements: Statement I: The minimum distance at which all three workers will step on the same spot again is 21 meters and 60 centimetres. Statement II: The LCM of their step lengths is 2520 cm. Select the correct answer from the options below: (a) Only Statement I is correct. (b) Only Statement II is correct. (c) Both Statements I and II are correct. (d) None of the Statements is correct.