5th Grade Word Problems on H.C.F. and L.C.M.

Here we will solve different types of word Problems on H.C.F. and L.C.M.

1. Find the lowest number which is exactly divisible by 20, 30 and 48.

Solution:

We find the L.C.M. of 20, 30 and 48.

2 |20, 30, 48

2 |10, 15, 24

3 |  5, 15, 12

5 |  5,  5,  4

      1,  1,  4

The L.C.M. of 20, 30 and 48 is 2 × 2 × 3 × 5 × 4 = 240.

Therefore, the lowest number which is exactly divisible by 20, 30 and 48 is 240.

2. Find the smallest number which when divided by 8, 24 and 32 when leaves 7 as remainder in each.

Solution:

First, we find the L.C.M. of 8, 24 and 32.

So, the L.C.M. is 2 × 2 × 2 × 3 × 4 = 96.

Therefore, the required number = 96 + 7 = 103

3. Find the greatest four-digit number which is exactly divisible by 25, 40 and 60.

Solution:

First, we find the L.C.M. of 25, 40 and 60.

L.C.M. = 2 × 2 × 5 × 5 × 2 × 3 = 600.

We know, the greatest four-digit number is 9999.

We divide 9999 by the L.C.M. of the number.

Therefore, the greatest four-digit number which is exactly divisible by 25, 40 and 60 = 9999 - 399 = 9600

Worksheet on Word problems Based on L.C.M. and H.C.F.

1. Find the smallest four-digit number which is exactly divisible by 30, 65, 90.

2. Find the greatest four-digit number which leaves no remainder when divided by 15, 21 and 28.

3. Find the smallest number which leaves 5 as remainder when divided by 37 and 87.

4. Find the smallest number which leaves 5 as remainder when divided by 14, 21 and 35.

5. Find the greatest one digit number which divides 15, 25 and 40 exactly.

6. Find the greatest three digit number which is exactly divisible by 10, 20 and 30.

7. Three bulbs glow at regular intervals of 14, 20 and 24 seconds. When will they glow together?

8. Find the greatest number which divides 125, 150 and 300 exactly when increased by 4.

9. Three bells ring at regular intervals of 8, 10 and 12 minutes. If they ring together at 6.00 a.m., when will they ring together again?

10. David has some bottles which he can arrange in rows of 4, 7 or 14. What is the least number of bottle which can be arranged in this manner?

5th Grade Word Problems on H.C.F. and L.C.M.

Answer

1. 1170

2. 9660

3. 3224

4. 215

5. 5

6. 960

7. 840 sec.

8. 21

9. 8. am

10. 28

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