Question

2. If a =(2^2 x 3^3 x 5^4) and b = (2^3 x 3^2 x 5) then HCF(a, b) =?​

Answer 1

Answer:

HCF = 360

LCM = 135000

Step-by-step explanation:

HCF is the highest common factor of multiple number

a = 2²×3³×5⁴ and b = 2³×3²×5

so their common factor is 2²×3²×5 (since these are the common terms in their prime factorisation)

=> HCF = 8×9×5 = 360

for two numbers, their product is equal to the product of their HCF and LCM

=> 2²×3³×5⁴ × 2³×3²×5 = 360 × LCM

=> 2²×3³×5⁴×2³×3²×5 = 2²×3²×5 × LCM

=> LCM = 2⁵×3⁵×5⁵ / (2²×3²×5) = 2³×3³×5⁴ = 8×27×625 = 13500