HCF and LCM
Q. Find HCF and LCM of the following:
a. 16(a2+2a-3), 24(a2+a-6), 48(a2-a-12)
Soln:
1st expression: 16 ( a2 +2a-3)
= 8*2 [a2+(3-1) a-3]
= 8*2 [a2+ 3a-a-3]
= 8*2 [a (a+3) - 1(a+3)]
= 8*2 (a-1) (a+3)
2nd expression: 24(a2+a-6)
= 8*3[a2+ (3-2)a - 6]
= 8*3[ a2+ 3a-2a-6]
= 8*3[ a(a+3)-2(a+3)]
= 8*3 (a+3) (a-2)
3rd expression: 48(a2-a-12)
= 8*3*2 [ a2-(4-3)a-12]
= 8*3*2[a2- 4a-3a-12]
= 8*3*2[a(a-4)+ 3(a-4)]
= 8*3*2(a+3)(a-4)
Therefore, H.C.F = 8 (a+3)
And L.C.M= 8*3*2(a-1) (a-2) (a+3) (a-4)
= 48(a-1) (a-2) (a+3) (a-4)