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

Answer 1

(i) 12, 15 and 21 

12 = 2 × 2 × 3 

15 = 3 × 5 

21 = 3 × 7 

∴ H.C.F. = 3 

L.C.M. = 3 × 2 × 2 × 5 × 7 = 420 

∴ HCF × LCM = Product of three numbers 

3 × 420 = 12 × 15 × 21 

1260 = 1260

(ii) 17, 23 and 29 

17 = 17 × 1 

23 = 23 × 1 

29 = 29 × 1 

∴ H.C.F. = 1 

L.C.M. = 17 × 23 × 29 = 11339 

∴HCF × LCM = Product of three numbers 

1 × 11339 = 17 × 23 × 29 

11339 = 11339 

(iii) 8,9 and 25 8 = 2 × 2 × 2= 23 

9 = 3 × 3 = 32 

24 = 5 × 5 = 52 

∴ H.C.F. = 1 

L.C.M. = 2³ × 3² × 52 = 8 × 9 × 25 = 1800 

∴ HCF × LCM = Product of three numbers 

1 × 1800= 8 × 9 × 25 

1800 = 1800