How many numbers are there from 300 to 700 wh | vedclass

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(C) To find numbers divisible by $2, 3,$ and $7$,we must find the Least Common Multiple $(LCM)$ of these numbers.Since $2, 3,$ and $7$ are prime numbe

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$9$

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(C) To find numbers divisible by $2, 3,$ and $7$,we must find the Least Common Multiple $(LCM)$ of these numbers.Since $2, 3,$ and $7$ are prime numbers,their $LCM = 2 	imes 3 	imes 7 = 42$.We need to find the count of multiples of $42$ in the range $[300, 700]$.First,find the number of multiples of $42$ up to $700$: $\lfloor 700 / 42 floor = 16$.Next,find the number of multiples of $42$ up to $299$: $\lfloor 299 / 42 floor = 7$.The number of multiples between $300$ and $700$ is $16 - 7 = 9$.

How many numbers are there from $300$ to $700$ which are divisible by $2, 3,$ and $7$?

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