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Real Numbers

Question
CBSEENMA10006267
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Using prime factorization method, Find the LCM of

(i) 12, 15, 20, 27 (ii) 21, 28, 36, 45.

Solution
(i) 12, 15, 20, 27

Since, 12 = 2 × 2 × 3 = 22 × 3

15 = 3 × 5

20 = 2 × 2 × 5 = 22 × 5

and    27 = 3 × 3 × 3 = 33

∴ LCM = Product of each prime factor with highest power

= 22 × 33 × 5 = 540

i.e., LCM (12, 15, 20, 27) = 540.

(ii) 21, 28, 36, 45

 

Since, 21 = 3 × 7

28 = 2 × 2 × 7 = 22 × 7>

36 = 2 × 2 × 3 × 3 = 22 × 32

and    45 = 5 × 3 × 3 = 5 × 32

∴ LCM = Product of each prime factor with highest power

= 32 × 7 × 22 × 5

= 1260

i.e. LCM (21, 28, 36, 45)= 1260.

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