Question

Find the least square number , exactly divisible by each one of the numbers:
(i) 6,9,15 and 20 (ii) 8,12,15 and 20

Answer 1

(i) 6,9,15,20

LCM of 6,9,15,20= 2\times 3\times 5\times 3\times 2 =180
$2\times 2\times 3\times 3\times 5$
We see that afer grouping the factors in pairs 5 is left unpaired
$\therefore Leastperfectsquare=180\times 5=900$

(ii) 8,12,15,20
LCM of 8,12,15,20

= $2\times 2\times 2\times 3\times 5$
We see that after grouping the factors, factors2,3,5 are left unpaired
$\therefore Perfectsquare=120\times 2\times 3\times 5$
= $120\times 30=3600$