Find the smallest square number and which is divisible by each of the numbers 6,9 and 15.
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Answered by
1
Answer:
Step-by-step explanation:
Least number= LCM of 6,9,15=90so the square of 90 is divisible by 6,9,15 and also smallest square number
=8100
Answered by
17
Answer:
This has to be done in 2 steps.
- Find the smallest common multiple.
- Find the square number needed.
⇝The least number which is divisible by each of 6,9 and 15 is their LCM. The LCM of 6,9 and 15 is 2×3×3×5=90.
Prime factorisation of 90 is 2×3×3×5.
➝We see that Prime factors 2 and 5 are not in pairs. Therefore 90 is not a perfect square.
In order to get a perfect square,each factor of 90 must be paired.So we need to make pairs of 2 and 5.Therefore,90 should be multiplied by 2×5,i.e., 10.
Hence the required square number is 90×10=900.
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