Question

Find the L.C.M. Of 90, 108 and 144 by prime factorisation

method. plz give answer in full process by solving it I will make you brainlist​

Answer 1

Answer:

90=3×3×2×5

108=3×3×3×2×2

144=3×3×2×2×2×2

so the lcm of 90,108 and 144 is 3×3×2×2×2×2×5= 720

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Answer 2

The LCM of 90, 108, and 144 is 4320.

Given:

Three numbers: 90, 108, and 144.

To Find:

The LCM of 90, 108, and 144 by prime factorization method.

Solution:

The LCM is the smallest multiple of each of the given numbers.

To find the LCM of 90, 108, and 144, let us first write down their prime factorization.

90 = 2 × 3 × 3 × 5 = 2 x 3² x 5

108 = 2 × 2 × 3 × 3 × 3 = 2² x 3³

144 = 2 x 2 x 2 x 2 x 3 x 3 = $2^{4}$ x 3²

Now, the factors common to 90, 108, and 144 are 2 and 3.

Collect the highest factors of 2 and 3. This turns out to be  $2^{4}$ and 3³.

Then collect the terms that are unique to each of the given numbers. Here, the unique term is 5.

Their product gives us the LCM.

So, LCM of 90, 108, and 144 =  $2^{4}$  x 3³  x 5 = 2160.

∴ The LCM of 90, 108, and 144 is 2160.

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