how many numbers are divisible by 4 6 8 upto 450
Answers
Answer:
18 numbers are divisible by 4 6 8 upto 450
Step-by-step explanation:
numbers divisible by 4 6 8
Lets find LCM of 4 , 6 & 8
4 = 2 * 2
6 = 2 * 3
8 = 2 * 2 * 2
LCM = 2*2 *2 *3 = 24
Number Divisible by 24 would be divisible by 4 , 6 & 8
24 , 48 , ................................................................408, 432
24*1 , 24*2 ........................................................24*17 , 24*18
18 numbers are divisible by 4 6 8 upto 450
Answer:
If we took the series from 8 upto 450 and the numbers are 4 and 6 then the answer is different but when we took the series of 1 upto 450 and the numbers are 4,6 and then the answer is different.I am explaining both.
Step-by-step explanation:
when the series starts from 8 upto 450 and numbers are 4 and 6 then
we first take LCM of 4 and 6
4=2*2
6=2*3
LCM=2*2*3=12 Now
12*1=12 It is in between 8,9,10.............450
12*2=24
similarly it will go upto 37 because
12*37=444
When we multiply it with 38 then it exceeds from the series such as 12*38=456 so the number 456 is not in between 8,9,10.............450
so According to AP
a(n)=a(1)+(n-1)d
a(n)=444
a(1)=12
d=12
As a(1)=d so the answer will be 37
ANOTHER WAY OF THINKING
when the series starts from 1 upto 450 and numbers are 4,6 and 8 then
we first take LCM of 4,6 and 8
4=2*2
8=2*2*2
6=2*3
LCM=2*2*2*3=24 Now
24*1=24 It is in between 1,2,3.............450
24*2=48
similarly it will go upto 18 because
=432
When we multiply it with 19 then it exceeds from the series such as 24*19=456 so the number 456 is not in between 1,2,3.............450
so According to AP
a(n)=a(1)+(n-1)d
a(n)=432
a(1)=24
d=24
As a(1)=d so the answer will be 18