can two numbers have 16 as hcf and 380 as lcm
Answers
Answered by
19
no there can't be any number have 16 HCF and 380 as LCM .
#Reason:-
we know that product of two number is equal to the product of their HCF and LCM
let two numbers be a and b
then a×b =HCF ×LCM
a×b=16×380
now for 16 to be the HCF of a and b ,both a and b must be the multiple of 16
let a be the smallest multiple of 16 ,that is 16 itself
so 16 × b = 16× 380
this gives b is 380
so a is 16 and b is 380
but the HCF of these two numbers is 4 not 16
Thus, a cannot be equal to 16 .also if we take any bigger multiple of 16 then also we will arrive at a contradiction .
does we come to the conclusion that there cannot be any two numbers whose HCF is 16 and LCM is 380 .
hope this answer will be helpful to you
if any doubt you can reply me back
#Reason:-
we know that product of two number is equal to the product of their HCF and LCM
let two numbers be a and b
then a×b =HCF ×LCM
a×b=16×380
now for 16 to be the HCF of a and b ,both a and b must be the multiple of 16
let a be the smallest multiple of 16 ,that is 16 itself
so 16 × b = 16× 380
this gives b is 380
so a is 16 and b is 380
but the HCF of these two numbers is 4 not 16
Thus, a cannot be equal to 16 .also if we take any bigger multiple of 16 then also we will arrive at a contradiction .
does we come to the conclusion that there cannot be any two numbers whose HCF is 16 and LCM is 380 .
hope this answer will be helpful to you
if any doubt you can reply me back
Answered by
1
Answer
no
Step-by-step explanation:
16 and 380 are coprimes
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