Question

The circumferences of three wheels are 120 cm,
75 cm, and 75 cm respectively. What is the least
distance covered by the three wheels so that each
makes a complete number of revolutions?​

Answer 1

✬ Least Distance = 600 cm ✬

Step-by-step explanation:

Given:

• Circumference of first wheel is 120 cm , second wheel is 75 cm & third wheel is 75 cm.

To Find:

• What will be least distance covered by wheels for making a complete no. of revolutions ?

Solution: To find the least distance we need to find the LCM.

➟ LCM of 120 , 75 , 75

• 3 [ 120, 75 , 75
• 5 [ 40 , 25 , 25
• 5 [ 8 , 5 , 5
• [ 8 , 1 , 1

So,

$\implies{\rm }$ LCM = 3 $\times$ 5 $\times$ 5 $\times$ 8

$\implies{\rm }$ LCM = 15 $\times$ 40

$\implies{\rm }$ LCM = 600

Hence, the required least distance is 600 cm.

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★ LCM (full form Least Common Factor) is a group of numbers which is the smallest number that is a multiple of all the numbers.

Answer 2

${\huge{\bf{\blue{Solution:-}}}}$

Given:-

⇢ The circumferences of three wheels are 120 cm, 75 cm, and 75 cm respectively.

ㅤ

Find:-

⇢ What is the least distance covered by the three wheels.

ㅤ

Calculations:-

⇢ Taking Least Common Multiple (LCM) we can find the required least distance.

ㅤㅤ

⇢ $\sf{(3 \times 5) \times (5 \times 8)}$

⇢ $\sf{15 \times 40}$

⇢ ${\boxed{\bold{LCM = 600 \: cm}}}$

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Therefore, 600 cm is the least distance required.