Question : How many numbers between 400 and 700 are divisible by 5, 6 and 7?
Option 1: 20
Option 2: 10
Option 3: 2
Option 4: 5
Correct Answer: 2
Solution : LCM of 5, 6, and 7 = 210 Quotient when 400 is divided by 210 ⇒ $\frac{400}{210}$ ⇒ 1 Quotient when 700 is divided by 210 ⇒ $\frac{700}{210}$ ⇒ 3 Total number of multiples of 210 between 400 and 700 = 3 – 1 = 2 So, the numbers between 400 and 700 that are divisible by 5, 6 and 7 = 2 Hence, the correct answer is 2.
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