Question.
Find the LCM and HCF of the following integers by applying the prime factorisation method
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
Find the LCM and HCF of the following integers by applying the prime factorisation method
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
Solution:
(i) 12,15 and 21
So, $12=2 \times 2 \times 3=2^{2} \times 3$
So, $15=3 \times 5$
So, $21=3 \times 7$
Therefore
$\mathrm{HCF}(12,15,21)=3 ;$
$\mathrm{LCM}=(12,15,21)=2^{2} \times 3 \times 5 \times 7=420$
(ii) $17,23,29$
$17=1 \times 17$
$23=1 \times 23$
$29=1 \times 29$
$\mathrm{LCM}=1 \times 17 \times 23 \times 29$
$\mathrm{HCF}=1$
(iii) $8,9,25$
$8=2 \times 2 \times 2$
$9=3 \times 3$
$25=5 \times 5$
$\mathrm{LCM}=2^{3} \times 3^{2} \times 5^{2}$
$\mathrm{HCF}=1$
(i) 12,15 and 21
So, $12=2 \times 2 \times 3=2^{2} \times 3$
So, $15=3 \times 5$
So, $21=3 \times 7$
Therefore
$\mathrm{HCF}(12,15,21)=3 ;$
$\mathrm{LCM}=(12,15,21)=2^{2} \times 3 \times 5 \times 7=420$
(ii) $17,23,29$
$17=1 \times 17$
$23=1 \times 23$
$29=1 \times 29$
$\mathrm{LCM}=1 \times 17 \times 23 \times 29$
$\mathrm{HCF}=1$
(iii) $8,9,25$
$8=2 \times 2 \times 2$
$9=3 \times 3$
$25=5 \times 5$
$\mathrm{LCM}=2^{3} \times 3^{2} \times 5^{2}$
$\mathrm{HCF}=1$
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