CBSE Class 10 Maths Fundamental Theorem of Arithmetic

Solution

64 = 1 × 2 × 2 × 2 × 2 × 2 × 2

80 = 1 × 2 × 2 × 2 × 2 × 5

Common factors of 64 and 80 = 1, 2, 2, 2, 2

Highest common factor of 64 and 80 = 2 × 2 × 2 × 2 = 16

Solution

Product of two numbers is equal to the product of their HCF and LCM. 

Solution

To find the LCM, multiply all the prime factors, but the common factors are included only once. 

36 = 2 × 2 × 3 × 3 = 2² × 3²

14 = 2 × 7

LCM = 2² × 3² × 7 = 2 × 2 × 3 × 3 × 7 = 252The required least common multiple (LCM) of 36 and 14 = 252.