Find the greatest number of four digits which is divisible by 14, 30 and 42.
- A9780
- B9880
- C9870
- D9098
Solution & Step-by-step Explanation
First, find the Least Common Multiple (LCM) of 14, 30, and 42.
Prime factorization:
14=2×7
30=2×3×5
42=2×3×7
LCM(14,30,42)=2×3×5×7=210
The greatest 4-digit number is 9999. Now divide 9999 by 210 to find the remainder:
9999÷210=47 with a remainder of 129
Subtract the remainder from 9999 to get the required number:
Required Number=9999−129=9870
Prime factorization:
14=2×7
30=2×3×5
42=2×3×7
LCM(14,30,42)=2×3×5×7=210
The greatest 4-digit number is 9999. Now divide 9999 by 210 to find the remainder:
9999÷210=47 with a remainder of 129
Subtract the remainder from 9999 to get the required number:
Required Number=9999−129=9870