The LCM and HCF of 36, 45 and 72 by using prime factorization method is:

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L.C.M = 230 and H.C.F = 5

L.C.M = 540 and H.C.F = 7

L.C.M = 230 and H.C.F = 2

L.C.M = 360 and H.C.F = 9

answer is D.

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Detailed Solution

Given 3 numbers 36, 45 and 72.
Prime factorization of 36, 45, 72 is,
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Prime factors of 36, 45, 72 are,

36 = 2 × 2 × 3 × 3 45 = 3 × 3 × 5 72 = 2 × 2 × 2 × 3 × 3

The L.C.M of 36, 45, 72 is,

⇒ 2 × 2 × 2 × 3 × 3 × 5

⇒

360
The H.C.F of 36, 45, 72 is,

⇒

3²

⇒

9
Therefore, L.C.M of 36, 45, 72 is 360 and H.C.F is 9.
Hence, option 4 is correct.

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