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Home| Questions|Q 103995
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Priyanka Kashyap
Priyanka Kashyap
Asked: February 23, 20232023-02-23T15:09:27+05:30 2023-02-23T15:09:27+05:30In: Mathematics

What is the LCM of 18 and 36?

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    1. Varun Kumar
      2023-02-23T20:15:53+05:30Added an answer on February 23, 2023 at 8:15 pm

      To find the least common multiple (LCM) of 18 and 36, we can use several methods, such as prime factorization, listing multiples, or using the formula LCM(a,b) = (a x b) / GCF(a,b). Here, we will use the prime factorization method, which involves expressing both numbers as products of their prime factors and finding the least common multiple.

      To start, we can factor each number into primes:

      18 = 2 x 3 x 3
      36 = 2 x 2 x 3 x 3

      Then, we can identify the common and non-common prime factors of the two numbers. The common prime factors are 2 and 3, and the non-common prime factors are 2 and 3. To find the LCM, we need to take the highest power of each prime factor that appears in either factorization:

      The highest power of 2 that appears is 2^2 = 4.
      The highest power of 3 that appears is 3^2 = 9.
      Multiplying these highest powers together, we get:

      LCM(18, 36) = 2^2 x 3^2 = 36

      Therefore, the LCM of 18 and 36 is 36.

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