Question

Find the HCF and LCM of 10224 and 1608 using prime factorisation method.​

Answer 1

Answer:

Prime factors of 10224 = 2 × 2 × 2 ×2 × 3× 3 × 71= 2⁴ × 3² × 71¹

Prime factors of 1608 = 2×2×2×3 ×67 = 2³ × 3¹ × 67¹

HCF of 10224 and 1608 = 2³ × 3 = 8 ×3 = 24

HCF × LCM = Ist number × 2nd number

24 × LCM = 10224 × 1608

LCM = (10224 × 1608) / 24

LCM = 10224 × 67

LCM = 685008

Hence, the HCF of 10224 & 1608 is 24 & the LCM of 10224 & 1608 is 685008.

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Answer 2

Answer:

Thus,

10224 = 2 × 2 × 2 × 2 × 3 × 3 × 71

= 2^4 × 3^2 × 71

and 1608 = 2 × 2 × 2 × 3 × 67 (1/2)

Therefore, HCF of 10224 and 1608 = 2^3 × 3 × 67 (1/2)

and LCM of 10224 and 1608

= Product of two numbers/HCF

$= \frac{10224 \times 1608}{24} \\ \\ = 685008$

Therefore, HCF and LCM of 10224 and 1608 is 24 and 685008 respectively.