Get an idea on how to Solve Word Problems on Highest Common Factor and Least Common Multiple. Try to answer the LCM and HCF Questions available here on your own and then verify with ours. Read the Question Carefully and understand what is asked so that you won’t have any difficulty in solving the LCM and HCF Word Problems. Learn the tips & tricks to solve Highest Common Factor and Least Common Multiple Problems easily and answer the questions you come across in your exams with utmost confidence.

Also, Check:

- Worksheet on H.C.F. and L.C.M
- Relationship between H.C.F. and L.C.M
- Worksheet on Methods of H.C.F.and L.C.M.

## Word Problems Involving H.C.F and L.C.M

**Example 1.
**Find the multiple of 40 which is in between 400 and 500 where the digits at tens place and hundreds place are equal?

**Solution:**

Multiples of 40 are 40,80,120,160,200,240,280,320,360,400,440,480,520 etc.

Given the number is in between 400 and 500

Here the numbers between 400 and 500 are 400,440,480.

Also given the digits at tens place and hundreds place are equal.

Here 440 is the number which has the same digit at tens place and hundreds place are equal.

**Example 2.
**Vijay’s friend asked him to bring the same number of chocolates and biscuits. The store sells chocolates in packs of 50, biscuits in packs of 20. Find how many chocolates Vijay will buy from the store?

**Solution:**

The store sells chocolates in packs of 50, biscuits in packs of 20.

Vijay has to buy the same number of chocolates and biscuits.

Now we have to find the LCM of Chocolates and Biscuits.

i.e. LCM(50,20)

50=2 × 5× 5 =2 × 5

^{2}

20=2 × 2 × 5=2

^{2}× 5

LCM(50,20)=2

^{2}× 5

^{2}

=4 × 5=20

**Example 3.
**Find the least number of square tiles by which the floor of a room of dimensions 1223 cm, 634 cm can be covered completely?

**Solution:**

We require the least number of square tiles, so each tile must be of maximum dimension.

To get the maximum dimension of tile, we have to find the largest number that exactly divides 1873 cm,958 cm.

HCF(1223, 634)=1 cm

Hence, the side of a square tile is 1 cm.

Required no. of tiles= Area of the floor/Area of a square tile

=1223.634/1.1

=775382

**Example 4.
**Anjali goes to dancing classes every 5th day. Sandhya goes to the same dance class every 4

^{ th}day. How many days will they meet in the dance class in the month of July and august if we start counting from 1st July?

**Solution:**

Given,

Anjali goes to dancing classes every 5th day.

Sandhya goes to the same dance class every 4

^{th}day.

Then from starting the first day, the number of days when they meet=LCM(5,6)=30

So every 20

^{th}day they will meet.

They will meet only once on July 20.

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**Example 5.
**A certain no. of fruits are stored in groups of 2,4,6,8 with no fruit left behind. Find the no. of fruits?

**Solution:**

Given,

Fruits are stored in groups of 2,4,6,8.

No. of fruits=LCM(2,4,6,8)

=24 fruits

Hence, there are 24 fruits.

**Example 6.
**Sameera can jump 5 steps at a time and Nilima can jump 6 steps at a time. On which of the steps will both meet if both start jumping together?

**Solution:**

Given,

Sameera can jump at a time= 5 steps

Nilima can jump at a time= 6 steps

if both starts jumping together, they will meet=LCM(5,6)

=30

**Example 7.
**Satvika has music classes on alternate days, dance class once in 4 days, and yoga class once on 4 days. On the 1st of Dec, she had all the 3 classes. When will she have all the 3classes again?

**Solution:**

Given,

**Satvika has music classes on alternate days i.e. every second day.**

dance classes =4 days,

yoga classes=3 days

Satvika will have all the 3 classes =LCM(2,4,3)

=12

Hence, Satvika will have all three classes on 13th December.

**Example 8.**

50 boys and 30 girls went on an educational trip. The boys and girls have to be divided into separate smaller groups such that each group has the same number of boys and girls. What is the maximum number of students in each group such that no student is left out?

**Solution:
**Given,

**No. of boys went on a trip=50**

No. of girls went on a trip=30

Maximum number of students in each group=h.c.f(50,30)=2 × 5=10

=10

They are 10 groups each group consists of 5 boys and 3 girls.

The maximum number of students in each group is(5 +3=8) 8.

**Example 9.
**Find the least number of plants in a group such that they are planted in the rows of 5,10,15?

**Solution:**

To find the least number of plants first we have to find the LCM of(5,10,15).

LCM(5,10,15)=30

So we need 30 plants to be planted in rows of 5,10,15.

**Example 10.
**Find the largest number that divides 92,42 leaving 2 as the remainder?

**Solution:**

Given,

**The number divides 92 and leaves 2 as the remainder.**

S0 the number divides 92-2=90 exactly

The number divides 42 and leaves 2 as the remainder.

So the number divides 42-2=40 exactly

Now we have to find the HCF(90,40)

Therefore, the largest number is 10.

**Example 11.
**Find the largest number that divides 57, 27 leaving 7 as the remainder?

**Solution:**

Given,

**The number divides 57 and leaves 7 as the remainder.**

S0 the number divides 57-7=50 exactly

The number divides 27 and leaves 7 as the remainder.

So the number divides 27-7=20 exactly

Now we have to find the HCF(50,20)

Therefore, the largest number is 10.