How many numbers between 1 and 1000 are divisible by all number 2, 3, 4, 5 and 6?
Explanation
Correct Option - 1
divisible by 2,3,4,5 and 6
Concept Used:
LCM of given numbers will be divisible by all given numbers.
Formula Used:
tn = a +(n-1).d
where,
tn = last term
a = first term
n = total terms
d = difference between two consecutive terms
Calculation:
LCM of 2,3,4,5 and 6 is 60
⇒ given range = 1 to 1000
⇒ 1st number in the series is 60
and the last number will be 960
⇒ Terms will be 60,120,180,___,960.
⇒ As the above series in AP
(60)
⇒ To find the total numbers in AP,
we have
Tn= a +(n-1).d
⇒ 960 = 60 + (n-1)× 60
⇒ 960 = 60 + 60n - 60
⇒ 960 = 60n
⇒ n = 960/60
⇒ n = 16
∴ 16 numbers will be there.
