# HCF and LCM

## HCF(Highest Common Factor)

#### Common Factor:

A number is said to be a factor of another numbers when it divides other numbers exactly.

##### Example:
a) 12 and 30
The factors of 12 are: 1, 2, 3, 4, 6 and 12
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30
So the common factors of 12 and 30 are: 1, 2, 3 and 6

b) 15, 30, 45
The Common Factors of 15, 30 & 45 are: 3, 5 & 15

#### HCF of two or more numbers is the greatest number that divides each of them exactly.

H.C.F. is also called Greatest Common Divisor (G.C.D.)
##### Example:

From the Above Common Factor Example we can find HCF by finding greatest element of the set of common factors

a) 12 and 30
The factors of 12 are: 1, 2, 3, 4, 6 and 12
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30
So the common factors of 12 and 30 are: 1, 2, 3 and 6 -> 6 is the Highest number so it is HCF of 12 & 30.

b) 15, 30, 45
The Common Factors of 15, 30 & 45 are: 3, 5 & 15 -> 15 is the Highest number so it is HCF of 15, 30 & 45.

## LCM(Least Common Factor)

#### Common Multilple:

Common Multiple is number which is exactly divisible by each of the numbers under consideration.

##### Example:

Common Multiple of 3 & 5 are: 15, 30, 45, 60...

#### LCM:

LCM of two or more numbers is the least or smallest number which is exactly divisible by each of them.

##### Example:

a) 3 & 5

Common Multiple of 3 & 5 are: 15, 30, 45, 60... but smallest is 15 which is LCM of 3 & 5.

## Co-primes

Two numbers are said to be co-primes if their HCF is 1.

## Questions Asked from this Chapter:

#### Question Type 1: Based on ( LCM X HCF = First Number X Second Number )

The LCM of two numbers is 30 and their HCF is 5. One of the number is 10. The other is:
a) 20
b) 25
c) 15
d) 5

The Product of two numbers is 216. If the HCF is 6, Then their LCM is:
a) 72
b) 60
c) 48
d) 36

#### Question Type 4: Based on the Ratio of the Numbers

The ratio of two numbers is 3:4 and their HCF is 4. Their LCM is:
a) 12
b) 16
c) 24
d) 48

#### Question Type 5: Based on the Applications of LCM and HCF

HCF and LCM of two numbers are 7 & 140 respectively. If the numbers are between 20 & 45, the sum of the numbers is:
a) 70
b) 77
c) 63
d) 56

The HCF of two numbers is 8. Which of the following can never be their LCM?
a) 24
b) 48
c) 56
d) 60

#### Question Type 6: Based on Addition, Difference, Multiplication and Division of the Numbers

The sum of two numbers is 45. Their difference is 1/9 of their sum. Their LCM is:
a) 200
b) 250
c) 100
d) 150

The product of two numbers is 4107. If the HCF of the numbers is 37, the greater number is:
a) 185
b) 111
c) 107
d) 101

#### Question Type 7: Based on the Pairs of the Numbers

The HCF and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:
a) 4
b) 3
c) 2
d) 1
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