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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.