LCM and HCF of two integers

LCM of two numbers

Example 1: Find the LCM of 66 and 28 .

Find the prime factorization of the two numbers.

2 66

3 33

11 11

1

2 28

2 14

7 7

1

28 = 22 x 7

66 = 2 x 3 x 11

Any multiple of 66 will also have 2, 3 and 11 as its factors. Likewise any multiple of 28 well have 2 and 7 as its factors. The common multiple will have all the prime factors of the two numbers as its factors. Where a prime factor is found in both the two numbers, the highest power is taken. In this case 66 has 2 as a factor and 28 has 22 which means

22 will be taken for the calculation.

The LCM is therefore

22x3x7x11 =4x3x7x11=924

The LCM of 66 an 28 is 924

Example 2: Find the LCM of 20 and 24 .

Find the prime factorization of the two numbers.

2 20

2 10

5 5

1

20 = 2 x 2 x 5

2

2

2

3

24

12

6

3

1

= 22 x 5

24 = 2 x 2 x 2 x 3 =23 x 3

The LCM is 23 x 3 x 5 = 120

1

BJS Muyambo| brian@researchmatters.co.zw, +263779397464

Example 3: Find the LCM of 1240 and 5300.

Find the prime factorization of the two numbers.

2

2

2

5

31

1240

620

310

155

31

1

2

2

5

5

53

5300

2650

1325

265

53

1

1240 = 23 x 5 x 31

5300 = 22 x 52 x 53

LCM of 1240 and 5300 = 23 x 52 x 31 x 53 = 328 600

two HCfHCF of two numbers

Example 1: Find the HCF of 66 and 28

Find the prime factorization of the two numbers.

2 66

3 33

11 11

1

66 = 2x3x11

2 28

2 14

7 7

1

28 = 22x7

The HCF is the highest number which can divide into both 28 and 66 without leaving a remainder. Its factors are therefore factors of both 28 and 66. In this case we multiply the common factors, taking the lowest powers. There is only one common factor 2 and its lowest power is in the number 66.

The HCF of 66 and 28 is = 2.

2

BJS Muyambo| brian@researchmatters.co.zw, +263779397464

Example 2: Find the HCF of 20 and 24.

Find the prime factorization of the two numbers.

2 20

2 10

5 5

1

20 = 2 x 2 x 5

2

2

2

3

24

12

6

3

1

= 22 x 5

24 = 2 x 2 x 2 x 3 =23 x 3

The common factor is 2 and we take 2 in