21a4b4c5
The exponent on the b is 4.
Assume a, b and c are integers. The formula of the LCM of three numbers is: p1max(a,b,c)p2max(a,b,c)......prmax(a,b,c), where each pi to the max() tells you the maximum exponent of the prime of one of the terms. For instance: Find the LCM of 2, 3 and 4. 2 = 2 3 = 3 4 = 2² Then, the prime 2 with the max exponent is 2, so select 2². The prime 3 with the max exponent is 1, so select 3. Multiply these values altogether to obtain 2² x 3 = 12.
For any two numbers a and b if a is divisible by b then LCM(a,b) is a.48 is divisible by 6, so LCM(48,6) is 48.
a and b have no common prime factors. Their LCM is their product.
If the rational expressions have large exponent, then you need to factor out this way: (a + b)ⁿ = (a + b)(a + b)...(a + b) [So there are n "(a + b)" factors.] Here are the examples... (a + b)³ = (a + b)(a + b)(a + b) (a + b)4 = (a + b)(a + b)(a + b)(a + b)
Factor them. 2 x 2 x b x b = 4b2 2 x 3 x b x b x b = 6b3 Combine the factors, eliminating duplicates. 2 x 2 x 3 x b x b x b = 12b3, the LCM
The answer is a^2b^2, because the smallest exponent of the a's is 2 and the same thing with the b's. Therefore, that's the LCM (or least common multiple), because it is the smallest value the two terms share with one another. **When writing an exponent on a computer, you use a carrot (^) to represent the exponent.
LCM means least common multiple. It's the popular math topic to learn in elementary school course and number theory college course.To learn about LCM, you need to factor out each term. Then, select the prime factor with the maximum exponent in either the factors of the first or another. In simplest form:LCM = [a,b] = p1max(a,b)p2max(a,b).....pnmax(a,b) where pi are the prime factors of a and b."max(a,b) of the p's" means that you select the prime factor with the largest exponent out of the whole prime factors for each term you have factored out.
Assume a, b and c are integers. The formula of the LCM of three numbers is: p1max(a,b,c)p2max(a,b,c)......prmax(a,b,c), where each pi to the max() tells you the maximum exponent of the prime of one of the terms. For instance: Find the LCM of 2, 3 and 4. 2 = 2 3 = 3 4 = 2² Then, the prime 2 with the max exponent is 2, so select 2². The prime 3 with the max exponent is 1, so select 3. Multiply these values altogether to obtain 2² x 3 = 12.
If the exponent of the numerator is a and the exponent of the denominator is b then the crude exponent of their quotient is a-b. However, if the mantissa of the quotient is less than 1 then it needs to be brought into the range [1, 10) and in doing that, the exponent will become a-b-1.
If you have ab then a is the base and b the exponent
The LCM of and b does not equal the LCM of a and b - a.
lcm(a,b,c,d) = lcm(lcm(a,b,c),d) = lcm(lcm(a,b),lcm(c,d))
If you have a real number,a, and raise it to a power b we say a^b is a times itself b times. That is to say aaaaaaaa...aaa b times. a is the base and b is the exponent. So if b is an integer,... -3,-2,-1,0,1,2,3... ,then we have an integral exponent. Examples are 2^5 and 2^-3. An example that is NOT an integral exponent is 2^(1/2) since 1/2 is not an integer. Dr. ChuckIt means that the exponent is a whole number, for example 3, 0, or -5.
If A and B have no common factors other than one, the LCM is their product.
gcd(a,b) = 1, Since lcm is the multiple of a and b, a|lcm(a,b) =⇒ lcm(a,b) = ax b|lcm(a,b) =⇒ b|ax =⇒ ax = bq for q∈Z Since gcd(a,b) = 1,b |x and b≤x =⇒ ab ≤ ax ---→ (O1) However, ax is the least common multiple and ab is a common multiple of a and b, ax ≤ ab ---→ (O2) by (O1) and (O2) , ax = ab lcm(a,b) = ab
The LCM of a^2b and b^2c is a^2b^2c
If the exponent is b, then you move the decimal point b places to the right - inserting zeros if necessary.