This is similar to the often-used method to find the LCM of 2 numbers: you have to factor each monomial, and eliminate duplicate factors (factors that appear in both terms). An example might make this clearer.
LCM of x2 + 5x, and x2 + 6x + 1
Factoring each: x(x+5), and (x+1)(x+5)
Multiply all the factors, but use the common factor (x+5) only once: x(x+5)(x+1)
LCM[(13b3)3, 7b2] = LCM[2197b9, 7b2] = 2197*7*b9 = 15379*b9
lcm(8, 9) = 72. 8 = 2^3 9 = 3^2 lcm = 2^3 x 3^2 = 72
First you Prime Factorize the two (or more) numbers. The LCM of the two (or more) numbers must contain all the prime factors of the two (or more) numbers that made it. To find the LOWEST common multiple, for each prime factor, find from one of the numbers where the prime factor has the highest power. The highest powers of each prime multiply together to form the LCM of the numbers. e.g. LCM of 36 and 24 36 = (2^2)(3^2) 24 = (2^3)3 LCM = (2^3)(3^2) = 72
The LCM is: 120
The LCM is: 2,520
72(d^3)(e^2)72 is the LCM of 24 and 36.d^3 is the LCM of d and d^3.e^2 is the LCM of e^2 and e.
72y^3
72y
Example: 3x4y2 and 9x3y5 Treat the whole numbers normally. The LCM of 3 and 9 is 9. Choose the highest value of the variables. In this case, the LCM is 9x4y5
72y^3
96a^4
LCM[(13b3)3, 7b2] = LCM[2197b9, 7b2] = 2197*7*b9 = 15379*b9
The GCF is 7y^2.
You need at least two numbers to find an LCM.
Let's try one. 30x2y3z4 - 42x4y5z2 Do the numbers first. Factor them. 2 x 3 x 5 = 30 2 x 3 x 7 = 42 Combine the factors, eliminating duplicates. 2 x 3 x 5 x 7 = 210 For the variables, select the highest exponent. The LCM of the above expression is 210x4y5z4
Since 16x3 is a multiple of 4x, it is automatically the GCF of this problem.
Since 4 is a multiple of 2, it is automatically the LCM.