Find the least common multiple of 7 and 12
To find the least common multiple of 7 and 12, we need to find the smallest number that is divisible by both 7 and 12.
The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
The multiples of 12 are: 12, 24, 36, 48, 60, ...
From the list of multiples, we can see that 12 is a common multiple of 7 and 12. However, to find the least common multiple, we need to find the smallest number that is divisible by both 7 and 12.
The prime factorization of 7 is 7, and the prime factorization of 12 is 2 x 2 x 3.
To find the least common multiple, we need to find the highest power of each prime factor that appears in the prime factorizations of 7 and 12.
The highest power of 2 in the prime factorization of 12 is 2 x 2 = 4, and the highest power of 3 in the prime factorization of 12 is 1.
Therefore, the least common multiple of 7 and 12 is 2 x 2 x 3 x 7 = 84.
The least common multiple of 7 and 12 is 84.