How many numbers between 150 and 500 are divi | vedclass

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(B) number divisible by $2, 3,$ and $7$ must be divisible by their $L.C.M.$Since $2, 3,$ and $7$ are prime numbers,their $L.C.M. = 2 	imes 3 	imes 7

Vedclass · Accepted Answer

$8$

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(B) number divisible by $2, 3,$ and $7$ must be divisible by their $L.C.M.$Since $2, 3,$ and $7$ are prime numbers,their $L.C.M. = 2 	imes 3 	imes 7 = 42.$We need to find the number of multiples of $42$ between $150$ and $500$.First,find the smallest multiple of $42$ greater than $150$: $42 	imes 4 = 168$.Next,find the largest multiple of $42$ less than $500$: $500 \div 42 \approx 11.9$,so $42 	imes 11 = 462$.The multiples are $42 	imes 4, 42 	imes 5, \dots, 42 	imes 11$.The number of such terms is $11 - 4 + 1 = 8$.

How many numbers between $150$ and $500$ are divisible by $2, 3,$ and $7$ together?

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