PROPERTIES OF LCM AND HCF
PROPERTIES OF HCF AND LCM
• HCF of co-prime numbers is 1
• LCM of given co-prime numbers is equal to the product of the numbers.
• The HCF of group of numbers is not greater than any of the given numbers.
• The LCM of a group of numbers is not less than any of the given numbers.
• The HCF of a group of numbers is always a factor of their LCM.
HCF OF CO-PRIME NUMBERS IS 1
EXAMPLES:
Consider 21 and 22
Consider 21 and 27:
The factors of 21 are 1, 3, 7 and 21.
The factors of 21 are 1, 3, 7 and 21.
The factors of 22 are 1, 2, 11 and 22.
Here 21 and 22 have only one
common factor that is 1. Hence, their
HCF is 1 and are co-prime.
The factors of 27 are 1, 3, 9 and 27.
Here 21 and 27 have two common
factors they are 1 and 3. HCF is 3 and
they are not co-prime.
LCM OF TWO CO-PRIME NUMBERS IS EQUAL TO THE
PRODUCT OF THE NUMBERS.
EXAMPLES
•
Consider 4 and 9
Factors of 4 are 1, 2 , 4
Factors of 9 are 1, 3, 9
4 and 9 are co primes
Prime factors of 4 and 9 are 2x2 and 3x3 respectively.
Therefore LCM of 4 and 9 is 36
And product of 4 and 9 is 36
HENCE PROVED
THE HCF OF GROUP OF NUMBERS IS NOT GREATER THAN
ANY OF THE GIVEN NUMBERS.
EXAMPLES:
• Consider 21 and 27:
• The factors of 21 are 1, 3, 7 and 21.
• The factors of 27 are 1, 3, 9 and 27.
• HCF of 21 and 27 is 3
• Therefore HCF 3 < 21,also 3 < 27
THE LCM OF A GROUP OF NUMBERS IS NOT LESS THAN
ANY OF THE GIVEN NUMBERS.
EXAMPLES:
• Consider 15 and 12
Prime factors of 15 - 3x5
Prime factors of 12 - 2x2x3
LCM = 2x2x3x5 = 60
Therefore LCM 60 > 12 and 60 >15
THE HCF OF A GROUP OF NUMBERS IS ALWAYS A
FACTOR OF THEIR LCM.
EXAMPLES:
•
Consider 6 and 12
Prime factors of 6 = 3x2
Prime factors of 12 = 3x2x2
Lcm of 6 and 12 = 3x2x2 = 12
Hcf of 6 and 12 = 6
Therefore 12/6 = 2
By this we can say that HCF is a factor of LCM.