When is the greatest common factor the same as the least common multiple?
482834
vamsich is right (and so is brainy every other thursday)\n\nGreatest common factor is ususally called "greatest common \ndivisor" or gcd.\n\nFor example gcd(5,10) = 5. The greatest common divisor of a set of numbers cannot be greater than the smallest number in the set.\n\nlcm(5,10)= 10. The least common multiple of a set of numbers cannot be less than the largest number in the set.\n\nSo the numbers must be equal if lcm = gcd. lcm(10,10)= gcd(10,10)=10
66482
use the formula: gcf(A,B)*lcm(A,B)=A*B\nIn this case A=8; B=x; gcf=1; lcm=24\nYou get 1*24=8x\n8x=24\nx=24/8\nx=3\n\nLittle task: give a reason for the formula...
317079
GCF=greatest common factor is the no that is the gteatest factor of two or more no is the GCF \n\nEX) 12=1,2,3,4,6,12\n    30=1,2,3,5,6,10,15,30\n\nAs you can see 6 is the greatest in here that is common with 12 and 30
686152
A common multiple of 2,3,4,5,6,9 and 10 is 64800. But that is not the lowest common multiple which would be a preferable answer. The lowest common multiple is the smallest of the common multiples of a given set of numbers,\n2 = 2 x 1\n3 = 3 x 1\n4 = 2 x 2\n5 = 5 x 1\n6 = 2 x 3\n9 = 3 x 3\n10= 2 x 5\ntheir lowest common multiple would be\n2 x 2 x 3 x 3 x 5 = 180\n180 would be the most ideal answer
1162826
Least common denominator is (x-3)(x+3).\n\n2/(x-3)(x+3) + 3*(x-3)/(x-3)(x+3)\n\n(2+3x-9)/(x-3)(x+3)\n\n(3x-7)/(x-3)(x+3).
947409
You mean LCM?  LCD is lowest common denominator.\n\nFor each number that you are trying to find the LCM for, break the number down into its prime factors (recall that the primes are 2, 3, 5, 7, 11, 13, 17, etc.), then gather the highest prime factor of each prime.\n\nAn example will work better here.  Let's try this:  Find the LCM of 9, 12 and 150.\n\nSTEP 1:  Get prime factors of each:\n9 = 3*3 = 3²\n12 = 2*2*3 = 2² * 3\n150 = 2*3*5*5 = 2 * 3 * 5²\n\nSTEP 2:  Take the highest prime factor of each prime:\n2 >> highest is 2² from 12\n3 >> highest is 3² from 9\n5 >> highest is 5² from 150\n7 >> we don't have any primes for 7 or higher, so we can stop\n\nSTEP 3:  Multiply the highest prime factors from step 2 together to get the LCM:\n\nLCM = 2² * 3² * 5² = 900\n\nHope that helped a little!\n\n~ ♥ ~
728450
G=(T+Mf)/M \ncross-multiply\nGM = T + Mf\nGM - Mf = T\nfactor out the M\nM(G - f) = T\nM = T(G-f)\n\nANSWER\nM = T(G-f)
628648
None. The two numbers have no common factors, bar -1. You mean exactly (with no remainder) not evenly.
549705
The factor 6y^2-3y can be factored further as 3y(2y-1).  Note that 3, a prime, becomes a purely scalar factor to the product of all three terms.\n\nThe gcf would be a monomial that divides into each of the three factors y, (2y-1) and (y+7).  But these are relatively prime (none can be divided into the others).  The only common factor of all three is 1.  This specifically means that y is not the gcf, and therefore 3y isn't the gcf, either.\n\nThis is analogous to a number being the product of 3 (or four) prime numbers.  Since none can divide into the others, the gcf of the product is 1.
889429
1) Yup. a_1 - 5 = a_2, so a_1 must be 3.\n2) What does the common ratio actually mean? Its any term divided by the term before it. So in this case, the common ratio is just (-3)/(-2) = 1.5. Now, how would you get the first term? To go from the first term to the second you'd multiply by 1.5; thus to go from the second to the first, divide by 1.5: -2/1.5 = -4/3 is the first term.
404099
1; that's the only number they have in common as a factor.  240 is the LCM (the other poster did the LCM instead of the GCF.)
696574
First figure the prime factors of each:\n88 / 2 = 44\n44 / 2 = 22\n22 / 2 = 11\n11 / 11 = 1\n\nSo 88 = 2 x 2 x 2 x 11\n\n104 / 2 = 52\n52 / 2 = 26\n26 / 2 = 13\n13 / 13 = 1\n\nSo 104 = 2 x 2 x 2 x 13\n\nThe common factors are all combinations of 2 x 2 x 2.\n\nThe common factors are therefore:\n1, 2, 4, 8 (several people forgot 1 as a common factor).\n\n(And the *greatest* common factor is 8.)
386935
42 = 2 * 3 * 7\n60 = 2 * 2 * 3 * 5\n\nSo, the GCF consists of the common ones, which are 2 * 3 = 6.
200143
Answering...\n\nSteps:\n1. Determine tha numbers/variables that are common to both terms.\n2. Use the greatest of these factors (GCF).\n3. Factor out the GCF.\n4. What are left, put them inside the parenthesis.\n\nTherefore:\n1. Common factor: 2\n2. GCF: 2\n3. and...\n4. 2(6y^2 - 5) ANSWER
335428
432 \n216 and 2 \n108 and 2\n54 and 2\n27 and 2 \n9 and 3\n3 and 3 \nThe least common is 3
787255
factors of 250 - 1, 2, 5, 10, 25, 50, 125, 250\n(a trick to know if u forgot one of them is to try multiplying the last number with the first number. ex) 1x250, 2x125, 5x50, 10x25)\n\nLCM of 135 and 63 - 8505 (thats 135 times 63, usually there's a number b4 that will divide evenly, but in this case, its the numbers multiplied together)\n\nLCM is the least number that can be divided evenly by both 135 and 63, 3 would be the LCD (least common denominator)
372976
yes u can\nt^2(s^4-4)is the factored form\nt^2 is the highest common factor\n\n\n75x^2 - 147y^2\n3 is the common factor\n3(25x^2-49y^2)\n3(5x^2-7y^2)(5x^2+7y^2) is the factored form of 75x^2 - 147y^2