5th Grade Least Common Factor (L.C.M.)

We already familiar with the least common multiple which is the smallest common multiple of the numbers. The least (lowest) common multiple of two or more numbers is exactly divisible by each of the given numbers.

Let us consider two numbers 12 and 15.

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 etc.

Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120 etc Common

multiples of 12 and 15 are 60, 120 etc.

Clearly, the least common multiple is 60.

So, the L.C.M. of 12 and 15 is 60.

We can find the L.C.M. of the given numbers as follows.

I: By Prime Factorisation Method

II: By Division Method

CASE I: Finding the L.C.M. by Prime Factorisation Method:

For Example:

1. Find the L.C.M. of 12, 15 and 24.

Solution:

Prime factors of 12 = 2 × 2 × 3

Prime factors of 15 = 3 × 5

Prime factors of 24 = 2 × 2 × 2 × 3

Here, 2 occurs a maximum number of 3 times and 3 and 5 occur once only

So, the L.C.M. of 12, 15 and 24 is 2 × 2 × 2 × 3 × 5 = 120

CASE II: Finding the L.C.M. By Division Method:

For Example:

1. Find the L.C.M. of 20, 30, 36.

Solution:

So, the L.C.M. of 20, 30, and 36 is 2 × 2 × 3 × 5 × 3 = 180.

NOTE: The L.C.M. of two prime numbers is their product.

For example, the L.C.M. of 3 and 7 is 3 × 7 = 21

If a number is the factor of another number, their L.C.M. is the greater number itself.

For example, the L.C.M. of 6 and 12 is 12.

Worksheet on 5th Grade Least Common Factor (LCM)

I. Find the L.C.M. of the following numbers by prime factorisation method.

1. 8 and 12

2. 90 and 180

3. 36 and 64

4. 44, 120 and 132

5. 24, 62 and 124

6. 180, 192 and 576

7. 36, 92 and 164

8. 20, 125 and 145

9. 18, 24 and 36

10. 14, 21 and 49

11. 27, 45 and 63

12. 50, 90 and 120

13. 38, 76 and 152

14. 28, 42 and 70

15. 60, 90 and 130

Answer:

I. 1. 24

2. 180

3. 64

4. 1320

5. 744

6. 2880

7. 33948

8. 14500

9. 72

10. 294

11. 945

12. 1800

13. 152

14. 420

15. 2340

II. Find the L.C.M. of following numbers by division method.

1. 24, 36 and 48

2. 8, 12 and 20

3. 68, 102 and 119

4. 15, 21 and 28

5. 55, 88 and 110

6. 39, 65 and 52

7. 66, 88 and 99

8. 54, 112 and 120

9. 56, 64 and 84

10. 63, 84 and 105

11. 60, 72 and 120

12. 95, 120 and 288

13. 225, 400 and 625

14. 78, 230 and 260

15. 120, 230 and 340

Answer:

II. 1. 144

2. 120

3. 1428

4. 420

5. 440

6. 780

7. 792

8. 15120

9. 1344

10. 1260

11. 360

12. 27360

13. 90000

14. 17940

15. 46920

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