Find the greatest 5 digits number that is divisible by 12, 24, 42 and 72
Answers
I think 80 is the answer.
To find:
The greatest 5-digit number that is divisible by 12, 24, 42 and 72
Step-by-step explanation:
To find the number that is divisible by 12, 24, 42 and 72, we find the least common multiple of these numbers.
- 12 = 2 × 2 × 3
- 24 = 2 × 2 × 2 × 3
- 42 = 2 × 3 × 7
- 72 = 2 × 2 × 2 × 3 × 3
Then least common multiple
= 2 × 2 × 2 × 3 × 3 × 7
= 504
So 504 is the least number that is divisible by 12, 24, 42 and 72.
To find the greatest 5-digit number that is divisible by 12, 24, 42 and 72, we divide the least 6-digit number by 504.
Here 100000 ÷ 504 has quotient = 198 and remainder = 208
So the required greatest number is (504 × 198) = 99792.
Final answer: 99792
The greatest 5-digit number that is divisible by 12, 24, 42 and 72 is 99792.
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