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Answer :
Final answer:
The L.C.M of 24 and 180 is 360 and the H.C.F is 12, found through prime factorization.
Explanation:
Firstly, we will find the prime factors of 24 and 180. The prime factors of 24 are 2, 2, 2, and 3. The prime factors of 180 are 2, 2, 3, 3, and 5. To find the Lowest Common Multiple (L.C.M), we consider all the factors, but only repeat common factors once. Therefore, the L.C.M of 24 and 180, based on these factors, would be 2 x 2 x 2 x 3 x 3 x 5 or 360.
To find the Highest Common Factor (H.C.F), we consider only the common factors. For 24 and 180, these would be two 2s and one 3, therefore their H.C.F is 2 x 2 x 3 or 12.
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