Notes on HCF and LCM | Grade 7 > Compulsory Maths > Operation on Whole Numbers | KULLABS.COM

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#### Highest Common Factor ( H.C.F)

The largest positive integer which divides two or more integers without any remainder is called Highest Common Factor (HCF). It is the possible factor of respective numbers.

To find H.C.F by Factorization method
At first, we should find the prime factors of the given number, then the product of the common prime factors is the H.C.F of the given numbers. For example:
Find the H.C.F of 30 and 42
Solution,

Here,
30 = 2× 3× 5× 1
42 = 2× 3× 7× 1
∴ H.C.F = 2× 3× 1
= 6

To the H.C.F by division method
In this method, we divide the larger number by the smaller one and again the first remainder. So obtained divides the first divisor. The process is continued till the remainder becomes zero. The last divisor for which the remainder becomes zero and it is the H.C.F of the given numbers. For example:
Find the H.C.F of 30 and 42

#### Lower Common Multiple (L.C.M)

The lower common multiple is the lowest factor of respective numbers.

To find L.C.M by Factorisation method
At first, the prime factor of the given number are to be found out, then the product of the common prime factors and the remaining prime factors(which are not common) is the L.C.M of the given numbers. For example:
Find the L.C.M of 30 and 42

Here,
30 = 2× 3× 5
42 = 2× 3× 7
L.C.M = 2× 3× 5× 7
= 210

Division method
In this method, the given numbers are arranged in a row and they are successively divided by the least common factors till the quotient are 1 or prime numbers. Then, the product of these prime factors is the L.C.M of the given number. For example:

∴ L.C.M = 2× 3× 5× 5× 7
= 1050

1. The largest positive integer which divides two or more integers without any remainder is called Highest Common Factor (HCF).  It is the possible factor of respective numbers.
2. The lower common multiple is the lowest factor of respective numbers.
.

### Very Short Questions

Solution:

Here,
F(16) = {1, 2, 4, 8, 16}
F(24) = {1, 2, 3, 4, 6, 8, 12, 24}
F(32) = {1, 2, 4, 8, 16, 32}
Now,
F(16) ∩ F(24) ∩  F(32) = {1, 2, 4, 8}
∴ H.C.F. of 16, 24 and 32 is 8.

Solution:

Here,
28 ÷ 2 = 14 (remainder is 0)
14 ÷ 2 = 7 (remainder is 0)
Now,
28 = 2 × 2 × 7
42 = 2 × 3 × 7
70 = 2 × 5 × 7
∴ H.C.F = 2 ×  7 = 14

Solution:

Here,
28 ÷ 2 = 14 (remainder is 0)
14 ÷ 2 = 7 (remainder is 0)

42 ÷  2 = 21 (remainder is 0)
21 ÷  3 = 7 (remainder is 0)

70 ÷  2 = 35 (remainder is 0)
35 ÷  5 = 7 (remaindder is 0)
Now,
28 = 2 × 2 × 7
42 = 2 × 3 × 7
70 = 2 × 5 × 7
∴ H.C.F = 2 ×  7 = 14

Solution:

Here,
24 ÷ 2 = 12 (remainder is 0)
12 ÷ 2 = 6 (remainder is 0)
6 ÷ 2 = 3 (remainder is 0)

36 ÷ 2 = 18 (remiander is 0)
18 ÷ 2 = 9 (remainder is 0)
9 ÷ 3 = 3 (remainder is 0)

Now,
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
∴ L.C.M. = 2 × 2 × 3 × 2 × 3 = 72

Solution:

Here,
M(4) = {4, 8, 12, 16, 20, 24, 28, 32, 36, 20, 44, 48, . . . . . . . }
M(6) = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . . . . . . }
M(8) = {8, 16, 24, 32, 40, 48, 56, 64, 72, 880, . . . . . . }
Now,
M(4) ∩ M(6) ∩ M(8) = (24, 48, . . . . . . . }
∴ L.C.M. of 4, 6, 8 is 24.

Solution:

24 ÷ 2 = 12 (remainder is 0)
12 ÷ 2 = 6 (remainder is 0)
6 ÷ 2 = 3 (remainder is 0)

36 ÷ 2 = 18 (remainder is 0)
18 ÷ 2 = 9 (remainder is 0)
9 ÷ 3 = 3 (renmainder is 0)

48 ÷ 2 = 24 (remiander is 0)
24 ÷ 2 = 12 (remainder is 0)
12 ÷ 2 = 6 (remainder is 0)
6 ÷ 2 = 3 (remiander is 0)

Now,
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 ×  2 × 3
∴ L.C.M. = 2 × 2 × 2 × 3 × 3 × 2 = 144

0%
• ### The largest positive integer which divides two or more integers without any remainder is called ______.

whole number
integers
lowest common factor
highest common factor
• ### The lowest factors of a respective number is known as ______.

lowest common factor
highest common factor
integers
lowest common multiple

20
5
10
100

60
12
3
4

134
143
153
192

54
34
28
12

90
60
120
30

6
24
12
18

100
75
300
50

260
280
240
220

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