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Secondary 1 | Maths
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Written as a product of its prime factord, 2475 = 3^2 × 5^2 × 11
The LCM of 2475 and 270, giving your answer as the product of its prime fators,
The greatest integer that will divide both 2475 and 270 exactly,
Find the value of n if 270n is a perfect square.
Date Posted: 5 years ago
Views: 807
i)
270 = 3 x 3 x 3 x 5 x 2 = 3³ x 5 x 2
2475 = 5² x 3² x 11
The LCM would be :
5² x 3³ x 11 x 2 = 14850
270 = 3 x 3 x 3 x 5 x 2 = 3³ x 5 x 2
2475 = 5² x 3² x 11
The LCM would be :
5² x 3³ x 11 x 2 = 14850
ii)
Greatest integer that will divide 2475 and 270 exactly is actually just the HCF
HCF = 3² x 5 = 9 x 5 = 45
Greatest integer that will divide 2475 and 270 exactly is actually just the HCF
HCF = 3² x 5 = 9 x 5 = 45
270 is a perfect square means :
3³ x 5 x 2 x n is a perfect square
The powers of all the prime factors should be even for it to be a perfect square.
3³ x 3 = 3⁴
5 x 5 = 5²
2 x 2 = 2²
So 270 can be 3⁴ x 5² x 2²
= (3² x 5 x 2) x (3² x 5 x 2)
= (3² x 5 x 2)²
= 90²
So n = 3 x 5 x 2 = 30
The question has not been phrased correctly. It should be asking for smallest value of n
3³ x 5 x 2 x n is a perfect square
The powers of all the prime factors should be even for it to be a perfect square.
3³ x 3 = 3⁴
5 x 5 = 5²
2 x 2 = 2²
So 270 can be 3⁴ x 5² x 2²
= (3² x 5 x 2) x (3² x 5 x 2)
= (3² x 5 x 2)²
= 90²
So n = 3 x 5 x 2 = 30
The question has not been phrased correctly. It should be asking for smallest value of n
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