Question

Find the LCM and HCF of the following integers by applying the prime factorisation method. 

1. \(12, 15\) and 
2.  \(17, 23\) and 
3. \(8, 9\) and \(25\)

Answer 1

(i) Numbers: \(12,15\) and \(21\)
Prime factorization of \(12 = 2^2 \times 3\)
Prime factorization of \(15 = 3 \times 5\)
Prime factorization of \(21 = 3 \times 7\)
Highest Common Factor (HCF) = \(3\)
Least Common Multiple (LCM) = \(2^2 \times 3 \times 5 \times 7 = 420\)

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(ii) Numbers: \(17,23\) and \(29\)
Prime factorization of \(17 = 1 \times 17\)
Prime factorization of \(23 = 1 \times 23\)
Prime factorization of \(29 = 1 \times 29\)
HCF = \(1\)
LCM = \(17 \times 23 \times 29 = 11339\)

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(iii) Numbers: \(8,9\) and \(25\)
Prime factorization of \(8 = 2 \times 2 \times 2\)
Prime factorization of \(9 = 3 \times 3\)
Prime factorization of \(25 = 5 \times 5\)
HCF = \(1\)
LCM = \(2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 1800\)