Page 52 - Math Skill - 5

50 Maths

Word Problems

Let’s Attempt
Example 1: Two containers are filled with 16 L and 24 L liquid. Find the capacity of the largest
container which can measure the liquid in both the containers in whole numbers.

Solution: Here, we have to find the HCF of 16 L and 24 L as we are required to find the
capacity of the largest container that can measure both the quantities of liquid.
Here, the required number should divide both 16 and 24 in whole numbers.

For finding HCF of 16 and 24, we must first find their prime factors.
16 = 2 × 2 × 2 × 2

24 = 3 × 2 × 2 × 2 Thus, HCF = 2 × 2 × 2 = 8.

Hence, a container of 8 L capacity can measure the liquid in both the given
containers completely.

Example 2: Find the least number which is divisible by each one of 8, 12 and 20.
Solution: Here, the least number divisible by 8, 12 and 20 is required to be found. It means
we are supposed to find the LCM of the given numbers.

2 8, 12, 20
2 4, 6, 10
2 2, 3, 5 Thus, LCM of 8, 12 and 20 = 2 × 2 × 2 × 3 × 5 = 120.
3 1, 3, 5 The least number which is divisible by 8, 12 and 20 is 120.
5 1, 1, 5

1, 1, 1
Example 3: Find the least number which when divided by any one of 5, 7 or 9 leaves 2 as the
remainder.
Solution: The problem involves finding the LCM of the given numbers.

3 5, 7, 9 LCM of 5, 7 and 9 = 3 × 3 × 5 × 7 = 315.
3 5, 7, 3 315 is the least number that is divisible by 5, 7 and 9. But we are
5 5, 7, 1 required to find a number that will leave 2 as remainder when
7 1, 7, 1 divided by any of the 5, 7 or 9. To get such a number, we must
1, 1, 1 add 2 to the LCM.

The required number is 315 + 2 = 317. The least number is 317.

Exercise 4.5

1. Three colour lamps of a traffic signal glow at intervals of 10, 12 and 15 seconds. After what
time, all three bulbs will glow together?
2. Three bells ring at intervals of 12, 15 and 18 minutes. They rang together at 10.30 a.m.
When will they ring together next?