The greatest three-digit number which is divisible by 14, 28, and 42 is:

Explanation

Given: 14, 28, and 42 Concept used: LCM is the smallest common multiple of two or more numbers. Calculation: 14 = 2 × 7 28 = 2 2× 7 42 = 2 × 3 × 7 LCM (14, 28, 42) = 2 2× 3 × 7 = 84 Largest three-digit number = 999 Quotient when 999 is divided by 84 = 999/84 = 11 Now, The greatest three-digit number which is divisible by 14, 28, and 42 = 11 × 84 ⇒ 924 ∴ The greatest three-digit number which is divisible by 14, 28, and 42 is 924. Shortcut Trick Option elimination method: Check the divisibility of 7. Since 3 digit no is divisible by 14, 28, and 42. So no will also be divisible by 7. Only 924 is divisible by 7.