Question

The greatest number of three digit which is divisible by 12, 30, and 50 is:

• A. 960
• B. 900
• C. 950
• D. 990

Answer 1

Answer:

B. 900

Greatest three digit number = 999

To find the divisible number, LCM of three number is require,

Factors of 12 = 3 $\times$ 4 = 2² $\times$ 3

Factors of 30 = 6 $\times$ 5 = 2 $\times$ 3 $\times$ 5

Factors of 50 = 25 $\times$ 2 = 2 $\times$ 5²

LCM of (12, 30, 50) = 2² $\times$ 3 $\times$ 5² = 300

On dividing 999 by 300, the remainder 99,

∴ Largest divisible number = 999 – 99 = 900.