**Red Traffic Light:**

It tells the drivers to STOP.

**Green Traffic Light:**

It tells the drivers to MOVE or continue moving.

**Yellow Traffic Light:**

It means the drivers GET READY, as the light will change to red.

The lights constantly change in the order:

Red, Green, Yellow.

The light changes from one colour to the other at regular intervals.

**Least Common Multiples (LCM):**

For any two or more numbers, the LCM is the smallest number that is divisible by all the numbers.

The least common multiples are written as LCM.

LCM is used to find the least time traffic lights at different crossings will light together.

**Example:**

The Traffic Lights at Three Different Road Crossings Change After Every 24 Seconds, 48 Seconds, and 72 Seconds Respectively. If the Light Changes Simultaneously at 8 P.M., Then at What Time Will It Change Again?

**Solution:**

Step 1:

The light change after every 24 seconds, 48 seconds, and 72 seconds.

Calculate the prime factorisation of 24, 48, and 72.

24 = 2 × 2 × 2 × 3

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

Step 2:

**What is the LCM of 24, 48, and 72?**

LCM = 2 × 2 × 2 × 2 × 3 × 3 = 144 The light of the traffic will change again after 144 seconds.

Step 3:

1 minute = 60 seconds.

When we divide 144 by 60, we get two as the quotient and 24 as the remainder.

Therefore, 144 seconds = 2 minutes and 24 seconds.

Hence, the light of the traffic will change at 8:02:24 p.m.

**Least Common Multiples**

**Question 1:**

Three Bells in the Temple Toll at Intervals of 48 Minutes, 72 Minutes, and 108 Minutes Respectively. If All of Their Toll at 6 A.M., What Time Will All of Them Toll Together Again?

**Solution:**

**Step 1:**

The bell rang at 48 seconds, 72 seconds, and 108 seconds respectively.

Calculate the prime factorisation of 48, 72, and 108.

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

**Step 2:**

Find the LCM of 24, 48, and 72.

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3

= 432

The bell will toll together after 432 minutes.

**Step 3:**

We know that 1 hour = 60 seconds.

When we divide 432 by 60, we get seven as the quotient and 12 as the remainder.

Therefore, 432 minutes = hours and 12 minutes.

Hence, at 1:07:00 p.m, the bell will toll together.

**Question 2:**

Rita and Her Three Other Friends Went to Three Different Road Crossings. They Observed That the Traffic Lights at Three Different Road Crossings Change After 6 AM Every 36 Seconds, 48 Seconds, and 72 Seconds Respectively. When does the Light Changes Simultaneously?

**Solution:**

**Step 1:**

After every 35 seconds, 70 seconds, and 119 seconds respectively, we can see the change in light.

Calculate the prime factorisation of 36, 48, and 72.

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

**Step 2:**

What is the LCM of 36, 48, and 72?

LCM = 2 × 2 × 2 × 2 × 3 × 3

= 144

So, after 144 seconds, the light will change together.

**Step 3:**

We know that 1 minute = 60 seconds.

When we divide 144 by 60, we get 2 as the quotient and 24 as the remainder.

Therefore, 144 seconds = 2 minutes and 24 seconds.

Hence, the light will change together at 6:02:24 AM.

**Factors and Multiplies Class 5**

**Question 3:**

The Priest in the Temple Rang Four Bells. The Four Bells Toll at Intervals of 12 Seconds, 15 Seconds, 18 Seconds, and 20 Seconds Respectively. If All of Them Toll at 8:20:00 Hours. What Time Will All of Them Toll Together Again?

**Solution:**

**Step 1:**

The light change after every 12 seconds, 15 seconds, 18 seconds, and 20 seconds.

Calculate the prime factorisation of 12, 15, 18, and 20.

12 = 2 × 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

20 = 2 × 2 × 5

**Step 2:**

Find the LCM of 12, 15, 18, and 20.

LCM = 2 × 2 × 3 × 3 × 5

= 180

The bell will toll together after 180 seconds.

**Step 3:**

We know that 1 minute = 60 seconds.

When we divide 180 by 60, we get 3 as the quotient and 0 as the remainder.

Therefore, 180 seconds = 3 minutes.

Hence, the bell will toll together at 8:23:00 hours.

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