Question

Find the hcf and lcm of 180 and 288 by prime factorization method

Answer 1

Heyaa☺
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LCM is 2×2^5×3^2×5=1440
HCF is 2^2×3^2=36.

Refer to above attachment.
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Answer 2

The HCF and LCM of 180 and 288 are 36 and 1440 respectively.

Given:

Two numbers, 180 and 288.

To Find:

The LCM and HCF of the given numbers.

Solution:

LCM of two numbers is the smallest number that is divisible by both numbers.

HCF of two numbers is the highest common factor present in the two numbers.

Let us resolve the given numbers into their prime factors.

180 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5

288 = 2 × 2 × 2 × 2 × 2 × 3 × 3 = $2^{5}$ × 3²

HCF can be found by multiplying the common factors.

⇒ HCF (288, 180) = 2²× 3² = 36

LCM can be found by computing the product of the highest number of times each of the prime factors occur.

⇒ LCM(180, 288) = $2^{5}$ × 3² × 5 = 1440

∴ The HCF and LCM of 180 and 288 are 36 and 1440 respectively.

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