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Mathematics Question on The Fundamental Theorem of Arithmetic

Find the LCM and HCF of the following integers by applying the prime factorisation method.

  1. 12,1512, 15 and
  2. 17,2317, 23 and
  3. 8,98, 9 and 2525
Answer

(i) 12,1512,15 and 2121
12=22×312=2^2×3
15=3×515=3×5
21=3×721=3×7
HCF =3= 3
LCM=22×3×57=420=2^2×3×57=420

(ii) 17,2317,23 and 2929
17=1×1717=1×17
23=1×2323=1×23
29=1×2929=1×29
HCF =1=1
LCM=17×23×29=11339=17×23×29=11339$$

(iii)** ** 8,98,9 and 2525
8=2×2×28=2×2×2
9=3×39=3×3
25=5×525=5×5
HCF=1= 1
LCM=2×2×2×3×3×5×5=1800=2×2×2×3×3×5×5=1800