pls answer with explanation
Answers
Answer:
First determine the prime factors needed:
10=2×5
12=2×2×3
15=3×5
18=2×3×3
So, you will need 22×32×5. That equals (65–√)2 , so you will need to multiply that by 5 in order to make it a perfect square of 302.
That's 900. Now to test that.
90010=90
90012=75
90015=60
90018=50
It's interesting though. If you divide out that extra factor of 5 as well, you are left with the original numbers.
905=18
755=15
605=12
505=10
Now to be precisely accurate though, the least square number that is divisible by the numbers provided is actually 02. But one that uses the factors from the numbers you provided specifically? That must be 302, or 900.
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10=2×5
12=22×3
15=3×5
18=2×32
the least number that is divisible by 10,12,15,18 is the lcm(10,12,15,18)=22×32×5
a number is a square iff all its prime factors are raised to even powers.
Note that expect 5 , all the other factors are already raised to even powers,
In order to make this product a square it should be multiplied by an odd power of 5
And to make the square the least,multiply the product by 51 (because 1 is the least positive integer),and then it becomes 22×32×52=900
The first step would be to identify the prime factors.
10 = 2*5
12 = 2*2*3
15 = 5*3
18 = 6*3 = 2*3*3
So you need a square number with factors 2, 3 and 5.
Which means you need two of each as factors.
You already have a five, two twos and two threes as factors. You need another 5.
The lowest square number divisible by 10, 12, 15 and 18 is:
2^2 * 3^2 * 5^2 = 900.
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