How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together?
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Take LCM of 2,3,7 that will be 42
Now the numbers witch are divisible by 42 will be divisible by 2,3,7
By A.P first number between 300 and 700 which is divisible by 42 is 336 and last is 672
So
672=336+(n-1)42
672-336=42n-42
336+42=42n
378/42=n
9=n
So 9 numbers between 300 and 700 which are divisible by 2,3 and 7
Now the numbers witch are divisible by 42 will be divisible by 2,3,7
By A.P first number between 300 and 700 which is divisible by 42 is 336 and last is 672
So
672=336+(n-1)42
672-336=42n-42
336+42=42n
378/42=n
9=n
So 9 numbers between 300 and 700 which are divisible by 2,3 and 7
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