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How many numbers between 400 and 800 are divisible by 4, 5 and 6 ?
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- 7
- 8
- 9
- 10
Correct Option: A
LCM of 4, 5 and 6 = 60
Quotient on dividing 800 by 60 = 13
Quotient on dividing 400 by 60 = 6
∴ Required answer = Quotient on dividing 800 by 60 – Quotient on dividing 400 by 60
∴ Required answer = 13 – 6 = 7
2nd Method to solve this question :
First number greater than 400
that is divisible by 60 = 420
Smaller number than 800 that
is divisible by 60 = 780
It is an Arithmetic Progression with common difference = 60
By tn = a + (n – 1)d
780 = 420 + (n – 1) × 60
⇒ (n – 1) × 60 = 780 – 420 = 360
⇒ (n – 1) = 360 ÷ 60 = 6
⇒ n = 6 + 1 = 7
