How many natural numbers below 860 are divisible by 5 and 11 but not by 3
if a number is to be divided by both 5 and 11, then it should also be divided by its LCM = 55
so, number of natural numbers below 860 that is divisible by 5 and 11 is 859/55 = 15 (ignore the fractional part)
of the 15 numbers that are multiples of 55, the numbers that are divisible by 3 are 3, 6, 9, 12 and 15 in other words ( 15/3 = 5)
so, 5 numbers are divisible by 3.
therefore the number of natural numbers which are divisible by 55 and not by 3 are = 15 - 5 = 10
if a number is to be divided by both 5 and 11, then it should also be divided by its LCM = 55
so, number of natural numbers below 860 that is divisible by 5 and 11 is 859/55 = 15 (ignore the fractional part)
of the 15 numbers that are multiples of 55, the numbers that are divisible by 3 are 3, 6, 9, 12 and 15 in other words ( 15/3 = 5)
so, 5 numbers are divisible by 3.
therefore the number of natural numbers which are divisible by 55 and not by 3 are = 15 - 5 = 10
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