if one of the given number is divisor of all the other,then it is the LCM of the given numbers true or false
Answers
Answer:
It's true
Step-by-step explanation:
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Answer:
True
Step-by-step explanation:
GCD and LCM:
When given any two integer numbers, both of the numbers are divisors of the LCM (least common multiple) of the two numbers, because the LCM is a multiple of each of the numbers. However, as long as the two numbers are not equal, then the LCM is never a divisor of both of the numbers. Also usually, the LCM of two numbers is higher than the greatest common divisor or GCD (greatest common divisor) of those numbers.
For Example, State whether the given statement is True or False :
Two numbers have 16 as their HCF and 380 as their LCM.
Solution:
We know that H.C.F. between the numbers is the ‘highest common factor between two numbers while L.C.M. is the ‘lowest common multiple’ of that numbers.
Two numbers with both H.C.F. as 16 and L.C.M. as 380 are not possible. 380 is the L.C.M. must be exactly divisible by 16 as their H.C.F.
i.e ( HCF of the numbers must be a factor of the LCM.)
Thus, L.C.M. 380 is ‘not divisible’ by H.C.F. 16 of two numbers. The given condition is not possible.
It is False.