How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? - published on 06 jul 15
a. 11
b. 12
c. 14
d. cannot be determined?
Answers
Answered by
5
Hey , sup!
As per the question,
LCM of 2,3,7 is 42 that means numbers between 100 to 600 that is divisible by 42 will also be divisible by 2,3,7 together.
a= 126. ( Lies in the range and a multiple of 42.)
d=42( because we need numbers divisible by 42.
l= 588(lies in the range and last digit divisible by 42 in the range.)
=> T(n)= a+(n-1)d.
=> 588=126+(n-1)42.
=> 588-126=(n-1)42.
=> 462=(n-1)42.
=> 462/42=n-1.
=> 11=n-1.
=> n=11+1=12.
So, there are 12 numbers between 100 and 600 that are divisible by 42.
Hope you understand and it helps.
As per the question,
LCM of 2,3,7 is 42 that means numbers between 100 to 600 that is divisible by 42 will also be divisible by 2,3,7 together.
a= 126. ( Lies in the range and a multiple of 42.)
d=42( because we need numbers divisible by 42.
l= 588(lies in the range and last digit divisible by 42 in the range.)
=> T(n)= a+(n-1)d.
=> 588=126+(n-1)42.
=> 588-126=(n-1)42.
=> 462=(n-1)42.
=> 462/42=n-1.
=> 11=n-1.
=> n=11+1=12.
So, there are 12 numbers between 100 and 600 that are divisible by 42.
Hope you understand and it helps.
Answered by
0
Answer:
(a) 11
Step-by-step explanation:
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