Find the LCM and HCF of the following integers by applying the prime factorisation method
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) $8,9,25$
$8=2 \times 2 \times 2$
$9=3 \times 3$
$25=5 \times 5$
$\mathrm{LCM}=2^{3} \times 3^{2} \times 5^{2}$
$\mathrm{HCF}=1$