CONCEPT OF HCF & LCM

 CONCEPT OF HCF & LCM

HCF (HIGHEST COMMON FACTOR):

HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers.

HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor (GCD).

STEPS FOR FINDING HCF :

STEP: 1 Write all the factors of the given numbers.

STEP: 2 Identify the common factors of the given numbers.

STEP: 3 Find the greatest common factor from them.

EXAMPLE 1 1:

Find the HCF of 8 and 12.

Factors of 8 = 1, 2, 4, 8

Factors of 12 = 1, 2, 3, 4, 6, 12

Common factors of 8 and 12 = 1, 2, 4

HCF of 8 and 12 = 4

EXAMPLE 2 1:

Find the HCF of 5, 10 and 15.

Factors of 5 = 1, 5

Factors of 10 = 1, 2, 5, 10

Factors of 15 = 1, 3, 5, 15

Common factors of 5, 10 and 15 = 1, 5

HCF of 5, 10 and 15 = 5

LCM (LEAST COMMON MULTIPLE):

LCM or least common multiple of two or more numbers is the smallest number which is a multiple of each of the numbers.

STEPS FOR FINDING LCM :

STEP: 1 Write the multiples of the given numbers.

STEP: 2 Identify the common multiples of the given numbers.

STEP: 3 Find the least common multiple from them.

EXAMPLE 1 1:

Find the LCM  of 4 and 8.

Multiples  of 4  = 4 , 8 , 12, 16, ….

Multiples of 8  = 8, 16, 24, 32, …..

Common multiples of 4 and 8 = 8, 16, ….

LCM of 4 and 8  = 8

EXAMPLE 2 1:

Find the LCM of 5, 10 and 15.

Multiples of 5 = 5, 10, 15, 20, 25, 30….

Multiples of 10 = 10, 20, 30, 40, 50 …..

Multiples of 15 = 15, 30, 45, 60, …

Common multiples of 5, 10 and 15 = 30, 60, ….

LCM  of 5, 10 and 15 = 30

worksheet pdf given below