12=22x3 15=3x5 So the LCM of 2, 12 and 15 is 22x3x5 = 60
the prime factorization of 12 in exponents is 2 to the second power times 3
22 x 3 = 12
2 x 2 x 2 = 8 2 x 2 x 3 = 12 2 x 2 x 2 x 3 = 24, the LCM
2 x 2 x 3 = 12 2 x 2 x 2 x 2 = 16 2 x 2 x 2 x 2 x 3 = 48, the LCM
The LCM of the given two numbers is 48
They are: 12 and 360 respectively
Two or more numbers are normally needed to find the LCM
To find the Least Common Multiple (LCM) of 12, 9, and 15, we first need to find the prime factorization of each number. The prime factorization of 12 is 2^2 * 3, the prime factorization of 9 is 3^2, and the prime factorization of 15 is 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^2 * 3^2 * 5 = 180. Therefore, the LCM of 12, 9, and 15 is 180.
That's a lot of extra work for this problem but here goes. 3 is already prime so it doesn't really have a factor tree or prime factorization. The prime factorization of 4 is 2 x 2 which looks like this in a factor tree.42,23 and 4 have no common prime factors, so the LCM is their product, 12
12=22x3 15=3x5 So the LCM of 2, 12 and 15 is 22x3x5 = 60
2 x 2 x 3 = 12 3 x 7 = 21 2 x 2 x 3 x 7 = 84, the LCM
the prime factorization of 12 in exponents is 2 to the second power times 3
2 x 2 = 4 2 x 3 = 6 2 x 2 x 3 = 12, the LCM
Since 36 is a multiple of 12, it is automatically the LCM, but if you insist... 2 x 2 x 3 = 12 2 x 2 x 3 x 3 = 36 2 x 2 x 3 x 3 = 36, the LCM
22 x 3 = 12
To find the LCM of 12, 30, and 150, we need to decompose the numbers into their prime factors. The prime factorization of 12 is 2^2 * 3, the prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 150 is 2 * 3 * 5^2. Now, we need to choose the common and uncommon prime factors with the highest exponent. The common prime factors are 2 and 3, and the uncommon prime factors are 5 and 2^2. Therefore, the LCM of 12, 30, and 150 is 2^2 * 3 * 5^2 = 300. [1]