Find The LCM And The HCF Of Integers

A - Find the LCM of two Numbers
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| [e-mail], [phone]

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| [e-mail], [phone]

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