Primes, HCF and LCM - Highest Common Factor and Its Applications
Primes, HCF and LCM - Highest Common Factor and Its Applications
TGM Original Questions
Find the highest common factor and lowest common multiple of the following
- \(2^3 \times 5^2 \times 7 \times 13^3\) and \(2^5 \times 3 \times 5 \times 7^3 \times 11\),
- \(3^3 \times 7^3 \times 13^4 \times 17^2 \times 23\) and \(2 \times 3^2 \times 5 \times 7^4 \times 11^2 \times 13^2 \times 17\),
- \(2^6 \times 3^2 \times 5^2 \times 7 \times 11^3\) and \(2^4 \times 3 \times 5 \times 11^2 \times 17^2\),
leaving your answer in index notation.
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Answer:(a) HCF \(=2^3\times5\times7\), LCM \(=2^5\times3\times5^2\times7^3\times11\times13^3\) (b) HCF \(=3^2\times7^3\times13^2\times17\), LCM \(=2\times3^3\times5\times7^4\times11^2\times13^4\times17^2\times23\) (c) HCF \(=2^4\times3\times5\times11^2\), LCM \(=2^6\times3^2\times5^2\times7\times11^3\times17^2\)
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