Find the smallest square number divisible by each of the numbers 35 and 12
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First, derive the prime factors for these numbers:
35 = 5*7
15 = 3*5
49 = 7*7
So any number divisible by all three would need to include all prime factors, with each factor that appears multiple times in any one number also occurring that many times.
So the least number divisible by all 3 is 3*5*7*7 = 735.
However, that is not a square number. To be square, each prime factor needs to occur an even number of times.
We're Ok with 7, but we need another 3 and another 5, which would give us 3*5*735 = 11,025. This is the square of 105.
The answer is 11,025.
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