Question

The greatest number of 3 digits which is divisible by 5, 15, 21 and 49 is :

• A. 715
• B. 765
• C. 785
• D. 735

Answer 1

Answer:

D. 735

735 is the greatest 3-digit number divisible by 5, 15, 21, and 49.

1. Find the LCM of the given numbers: 5, 15, 21, and 49.

   • Prime factorization of 5 = $5^1$

   • Prime factorization of 15 = $3^1 \times 5^1$

   • Prime factorization of 21 = $3^1 \times 7^1$

   • Prime factorization of 49 = $7^2$

   • $\text{LCM} = 3^1 \times 5^1 \times 7^2 = 3 \times 5 \times 49 = \mathbf{735}$

2. Find the greatest 3-digit multiple:

   • The greatest 3-digit number is 999.

   • Divide 999 by the LCM (735): $999 \div 735 = 1 \text{ with a remainder of } 264$.

   • Subtract the remainder from 999: $999 - 264 = \mathbf{735}$.