Question 26

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

Solution

L.C.M.(2,3,7) = 42

=> Numbers from 300 to 700 which are divisible by 42 are = 336,378,420,...,672

This is an AP with first term = $$a=336$$ and common difference = $$d=42$$

Let number of terms = $$n$$

=> Last term = $$a+(n-1)d=672$$

=> $$336+(n-1)42=672$$

=> $$(n-1)42=672-336=336$$

=> $$n-1=\frac{336}{42}=8$$

=> $$n=8+1=9$$

=> Ans - (C)

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