Lcm And Hcf

To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 48, 72, and 60, we first factor each number into prime factors: HCF (Highest Common Factor): The HCF is found by taking the lowest power of the common prime factors. The common prime factors are 2 and 3, and the lowest powers are and . Therefore, the HCF is: LCM (Least Common Multiple): The LCM is found by taking the highest power of each prime factor. The prime factors are 2, 3, and 5. The highest powers are , , and . Therefore, the LCM is: Thus, the HCF is and the LCM is .

The correct option is (B):

Correct answer: 6

Explanation:
We use the identity:


Given:
HCF = 5
Product = 30

So,


Hence, the LCM is 6.

The prime factorization of 196 is:

The sum of the exponents of the prime factors is:

Thus, the correct option is (D): 4

To find the HCF of 306 and 657, we'll use the Euclidean algorithm:

Step 1: Apply division algorithm to 657 and 306

Step 2: Now apply division algorithm to 306 and 45

Step 3: Apply division algorithm to 45 and 36

Step 4: Apply division algorithm to 36 and 9

Since the remainder is now 0, the HCF is the last non-zero remainder.

Conclusion

The HCF of 306 and 657 is (3) 9.