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      Question

      What are the Highest Common Factor and Lowest Common

      Multiple of 6, 72, 120?
      A 12, 180 Correct Answer Incorrect Answer
      B 6,360 Correct Answer Incorrect Answer
      C 360, 6 Correct Answer Incorrect Answer
      D 12,360 Correct Answer Incorrect Answer

      Solution

      First of all, let us perform the prime factorization of 6, we get, So, we get, 6 = 2Γ—3.....(i) Now, let us perform the prime factorization of 72, we get, So, we get, 72 = 2Γ—2Γ—2Γ—3Γ—3.....(ii) Now, let us perform the prime factorization of 120, we get, So, we get, 120 = 2Γ—2Γ—2Γ—3Γ—5......(iii) From equation (i), (ii) and (iii), we get, 6 = 2Γ—3 72 = 2Γ—2Γ—2Γ—3Γ—3 120 = 2Γ—2Γ—2Γ—3Γ—5 From the above three equations, we can see that the common factors of 6, 72, and 120 is 2Γ—3=6 So, we get the highest common factor or HCF of 6, 72, and 120 as 6. Now let us find the LCM of three numbers: 6, 72, and 120. We get, So, we get the LCM of 6, 72, and 120 as 2 Γ— 2 Γ— 2 Γ— 3 Γ— 3 Γ— 5 = 360 Hence, the LCM of the three numbers is 360

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