Find the lcm and hcf of 26 and 91

General
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find the lcm and hcf of 26 and 91

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Find the LCM and HCF of 26 and 91

Answer:
To find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 26 and 91, we need to follow these steps:

Solution By Steps:

  1. Prime Factorization:

    • First, we find the prime factorization of the two numbers.

      For 26:

      26 = 2 \times 13

      For 91:

      91 = 7 \times 13

  2. Highest Common Factor (HCF):

    • The HCF is found by identifying the common prime factors and selecting the lowest power of these factors that are common in both factorizations.

      In both 26 and 91, the only common prime factor is 13.

      Therefore, the HCF is:

      \text{HCF} = 13

  3. Least Common Multiple (LCM):

    • The LCM is found by taking all the prime factors present in both numbers, taking the highest power of these primes.

      The primes involved are 2, 7, and 13.

      Therefore, the LCM is:

      \text{LCM} = 2^1 \times 7^1 \times 13^1

    • Calculate the LCM:

      2 \times 7 = 14
      14 \times 13 = 182

Thus, we have:

  • HCF of 26 and 91 is \boxed{13}
  • LCM of 26 and 91 is \boxed{182}

This step-by-step method ensures we get the correct LCM and HCF by understanding the underlying prime factorizations and how to combine them properly.