Question

Find the HCF and LCM of the following given pairs of numbers by prime factorization,

i) 120, 90

ii) 50, 60

iii) 37, 49

Answer 1

i) 120, 90

We have 

120 = 2 × 2 × 2 × 3 × 5 

= 2³ × 3 × 5 

90 = 2 × 3 × 3 × 5 

= 2 × 3² × 5

∴ HCF = 2 × 3 × 5 = 30

LCM = 2³ × 3² × 5 = 360

ii) 50, 60

We have 

50 = 2 × 5 × 5 

= 2 × 5² 

60 = 2 × 2 × 3 × 5 

= 2² × 3 × 5

∴ HCF = 2 × 5 = 10 

LCM = 2 × 3 × 5 = 300

iii) 37, 49

We have 

37 = 1 × 37 

49 = 7 × 7 = 7² 

∴ HCF = 1 

LCM = 37 × 7² 

Note: H.C.F. of two relatively prime numbers is 1 and LCM is equal to product of the numbers.