Answer :
Final answer:
The Highest Common Factor (HCF) of 69 and 207 is the largest number that divides both numbers evenly, which is 3. The Least Common Multiple (LCM) of 69 and 207 is the smallest number that both numbers divide into evenly, which is 207. Therefore, the correct option is a. LCM = 207, HCF = 3.
Explanation:
The LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers can be found using different mathematical methods. In this case, we are finding the LCM and HCF of 69 and 207. The HCF, also known as the greatest common divisor, can be found by determining the largest number that divides evenly into both 69 and 207. The LCM can be found by determining the smallest number that both 69 and 207 divide into evenly.
To find the HCF of 69 and 207, we list the factors of each number: 69 (1, 3, 23, 69), 207 (1, 3, 69, 207). The largest number that appears in both lists is 3. So, the HCF of 69 and 207 is 3.
To find the LCM of 69 and 207, we want to find the smallest number that both numbers divide into evenly. The multiples of 69 are: 69, 138, 207, 276, 345, etc. Meanwhile, the multiples of 207 include: 207, 414, etc. Thus, the first common multiple of 69 and 207 is 207. Hence, the LCM of 69 and 207 is 207.
In conclusion, Option a. LCM = 207, HCF = 3 should be the correct option.
Learn more about LCM and HCF here:
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