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Ques:- The greatest four digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28
A. 9288
B. 9828
C. 9882
D. 9928
Right Answer:
To find the greatest 4-digit number which is exactly divisible by 12, 18, 21, and 28, follow these steps:
🟠 Step 1: Find the Least Common Multiple (LCM) of the numbers
We need the LCM of: 12, 18, 21, and 28
First, find their prime factorizations:
-
12 = 2² × 3
-
18 = 2 × 3²
-
21 = 3 × 7
-
28 = 2² × 7
Now take the highest powers of all prime numbers that appear:
-
2² (from 12 or 28)
-
3² (from 18)
-
7 (from 21 or 28)
LCM = 2² × 3² × 7 = 4 × 9 × 7 = 252
🟠 Step 2: Find the greatest 4-digit number divisible by 252
The largest 4-digit number is 9999
Divide 9999 by 252:
9999 ÷ 252 ≈ 39.682
So, take the whole number part → 39
Now multiply: 252 × 39 = 9828
✅ Final Answer:
The greatest 4-digit number exactly divisible by 12, 18, 21, and 28 is:
👉 9828
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