HCF of two numbers is always a factor of their LCM (True/False).
Answers
SOLUTION :
This statement HCF of two numbers is always a factor of their LCM is TRUE.
Because HCF is a factor of both the numbers which are factors of their LCM.
Hence, HCF of two numbers is always a factor of their LCM .
★★HCF : HCF of two or more numbers = product of the smallest power of each common prime factor involved in the numbers.
★★LCM = LCM of two or more numbers = product of the greatest power of each common prime factor involved in the numbers with highest power.
HOPE THIS ANSWER WILL HELP YOU...
Answer:
HCF of two numbers is always a factor of their LCM - Statement is TRUE!
Step-by-step explanation:
(i)
HCF(Highest Common Factor): It is the largest factor that divides two or more numbers.
Ex: HCF of 2,4 = 2.
(ii)
LCM(Least Common Multiple): It is the small number that is divisible by the set of given numbers.
EX: LCM of 2,4 = 2 * 2 = 4.
(iii)
Let us prove that HCF of two numbers is always a factor of their LCM
HCF of 18 and 36.
⇒ Prime factorization of 18 = 2 * 3²
⇒ Prime factorization of 36 = 2² * 3²
HCF(18,36) = 2 * 3²
= 18.
LCM(18,36) = 2² * 3²
= 36.
Clearly, it is proved that HCF of two numbers is always a factor of LCM.
Hope it helps!