
4
Let q(x) = -x**3 + x**2 + x + 1. Let b be q(0). What is the common denominator of 89/6 and ((-594)/20)/(2 + b)?
30
Suppose 0 = 2*y - 5*p + 17, -p - 5 - 6 = -4*y. Calculate the smallest common multiple of y and 3.
12
Let v(w) = -w**3 + 7*w**2 - 6*w - 7. Let s be v(5). What is the common denominator of -25/8 and (s/4)/(12/(-88))?
24
Suppose 11 - 35 = -3*t. Let q be 45/(-10)*(-8)/6. Let h(d) = d**2 - 5*d + 6. What is the lowest common multiple of h(q) and t?
24
Suppose 4*b + 3*i = -92, 0 = b - 3*i - 0*i + 8. Let j = 6453/5 + -1297. Find the common denominator of (-214)/b - (-4 + 3) and j.
10
Let t(w) = w**2 - 5*w + 1. Let s be t(5). Calculate the lowest common multiple of (-12 + 14)*s*4 and 8.
8
Calculate the common denominator of (-6)/(-14) - (-4237)/4389 and -82/33.
33
Let f = 6 - 3. Suppose -3*x + 2*x - f*z = -1, 5*x - 29 = -3*z. Suppose b + 1 = 0, 0*w - 3*w - 2*b = -22. Calculate the lowest common multiple of w and x.
56
Let b = 133393/12 + -11105. Calculate the common denominator of -55/18 and b.
36
Suppose -5*b = -c - 105, b = -3*b + 20. Calculate the common denominator of -2 + 1 + (-67)/10 and (1 + -3)/(45/c).
90
Suppose 36 = -13*x + 127. What is the least common multiple of x and 2?
14
Suppose p + 1 = -r + 2*p, 5*r = -4*p + 31. Suppose 0*d = r*d - 150. Suppose -d = -6*k + k. Calculate the lowest common multiple of 5 and k.
10
Suppose -3*t + 0*r + 36 = 4*r, -2*r + 58 = 4*t. Calculate the least common multiple of t and 5.
80
Let j = -8 + 11. Calculate the common denominator of (-933)/120 - j/5 and 31/20.
40
Let m(d) = -8*d + 2. Let i be (-1)/(1*3/6). Calculate the least common multiple of m(i) and 16.
144
Let w = -72/13 - 5/39. Find the common denominator of 55/7 and w.
21
Suppose 3*v - 3*l + 2*l + 14 = 0, 0 = -3*l + 6. Let j = 6 + v. Calculate the smallest common multiple of 12 - (j/(-1) - -3) and 5.
55
Let h(t) = t**3 - 14*t**2 - t + 16. Let q be h(14). Suppose -q*d + 10 = -6. Calculate the lowest common multiple of d and 20.
40
Let u = 6/499 + -14531/4990. Calculate the common denominator of 55/6 and u.
30
Let i(z) = -2 - 2*z**2 + 3 + 9*z + 3*z**2 + 0. Let t be i(-9). What is the least common multiple of 9 and (t + 1)*(-11)/(-2)?
99
Suppose 0 = 2*g - u - 1 - 6, -39 = -4*g - 3*u. Let l = g - 4. Calculate the common denominator of 2 + 154/20 - l and -19/4.
20
Suppose 0 = 7*a - 3*a + m - 20, 0 = 4*a + 3*m - 20. Suppose -a*w + 26 - 6 = 0. What is the least common multiple of w and 20?
20
Let m = -56 + 37. Let n = -13 - m. What is the least common multiple of 9 and n?
18
Calculate the common denominator of -62/21 and -2 + 8/2 - 86/(-36).
126
Let c(g) = g**2 - 2*g. Let v be c(3). Suppose -16 = -v*q - q. Calculate the lowest common multiple of q and (2 - (0 - 1)) + -2.
4
Let l = 1193/85 + -72/17. What is the common denominator of l and -68/9?
45
Let r(a) = -a**3 + 3*a**2 + 4*a - 4. Let q = -3 - -6. What is the lowest common multiple of 10 and r(q)?
40
Let u = -692 - -2709/4. Calculate the common denominator of u and (-11)/2*9/12.
8
Suppose 2*i - 48 = 6*i. Let m = i - -14. What is the lowest common multiple of m and 18?
18
Let f = -51035578186701398319876563917/634506810 + 80433460102187710639. Let p = 2/3732393 + f. Let s = p + -18/85. Find the common denominator of -2/7 and s.
14
Let c(p) = -p**3 + 12*p**2 + 15*p - 4. Calculate the smallest common multiple of 28 and c(13).
308
Let f = 15 - 9. What is the smallest common multiple of f and 10?
30
Suppose 0 = z + 4*z, 0 = k + z - 4. Suppose 9 + 3 = k*i. What is the smallest common multiple of 12 and 2/(-6)*(i + -15)?
12
Suppose 0 = 3*k + 2*c - 9, -2*k - 3*c = 2*k - 11. Suppose 14 = -k*r + 64. What is the lowest common multiple of r and 22?
110
Let g = -13 - -15. What is the lowest common multiple of g and 1?
2
Suppose 7 = -0*c + c. Calculate the common denominator of -12*(9/(-22))/(-3) and c/2*6/2.
22
Suppose i - 12 = -5*g + g, -4*g + 8 = 2*i. Suppose -g*s + 56 - 8 = 0. Calculate the lowest common multiple of s and 6.
12
Calculate the lowest common multiple of ((-12)/(-3))/(2/4) and 6.
24
Let r = -3 - -6. Let h = 2 + r. Suppose 2*z - 4*z + 2*j = -20, 0 = -h*j - 10. Calculate the least common multiple of 5 and z.
40
Suppose -5*n + 4*j + 22 = 3*j, 17 = n + 4*j. Calculate the least common multiple of n and 12.
60
Suppose 2*j - 4*j - 36 = -4*h, 5*h - 45 = -3*j. Calculate the least common multiple of h and 3.
9
Let k be 3/12 + 1150/8. What is the common denominator of -83/20 and 4/(-18) + (-625)/k?
80
Calculate the common denominator of (5 + -42)*2/9 and -59/10.
90
Find the common denominator of -22/19 and (-783)/(-18) + (-10)/4.
19
What is the common denominator of (2/(-4)*1)/(6/(-152)) and -43/15?
15
Let v be 6 - -379 - 1/(-1). Let o be (-6158)/(-4)*4/(-16). Let p = o + v. What is the common denominator of 85/22 and p?
88
Let l be ((-45)/5)/(35/(-6)). Let t = l + -7/5. Find the common denominator of t and (9/(-5))/(1/(-4)).
35
Suppose 0 = -5*u + 4*u + 2. Suppose u*c - 16 = -4*w + 2*w, -2*c - 6 = 0. Let v(d) = -11*d**3 + d + 1. Calculate the least common multiple of v(-1) and w.
11
Let s = -18749/804 + 14/201. What is the common denominator of 6/(-15) + 376/90 and s?
36
Let b = 41/18 - 20/9. Calculate the common denominator of -19/6 and b.
18
Suppose -3*f - 2 = -4*f. What is the lowest common multiple of 14 and f?
14
Calculate the common denominator of -17/12 and (-4)/(-38) + (-6454)/(-1140).
60
Let j be (-804)/(-30) + 8/(-10). Let h = 42 - j. What is the least common multiple of h and 22?
176
Suppose -78 = -4*c + 2. Suppose -c = -3*n - n. Calculate the lowest common multiple of n and 1.
5
What is the common denominator of 1/((-32)/3)*38 and ((-20)/12)/(4/6)?
16
Let l be 3*(-2)/37982*-33007. Let g = 1/5426 + l. Calculate the common denominator of 1/18 and g.
126
Calculate the least common multiple of (6/(-4))/(3/(-10)) and 9.
45
Suppose 0 = 2*x + 6, -h - 2*x - 31 = -6*h. What is the smallest common multiple of h and 10?
10
Suppose 4*g - 6*g + 1559 = -3*j, -j + 782 = g. Let r = 1631/2 - g. Calculate the common denominator of r and 137/12.
12
Let z = -2 - -5. Let t(o) = o**2 - 12*o - 10. Let l be t(13). Suppose -l*w + z*m = -21, w + m - 17 = -0*m. What is the common denominator of -71/10 and w?
10
Let n be (-3)/(24/(-4))*-4. Suppose 0 = 7*k - 2*k + 5, -2*j + 16 = -2*k. What is the least common multiple of (3 + n + 0)*5 and j?
35
Let o = 89 + -175. Calculate the common denominator of -1/4 and o/18 + (-6)/(-9).
36
Suppose -2 = -4*i + 3*i. Suppose -8 + 2 = -i*c. Find the common denominator of 23/8 and (7/c)/(20/(-12)).
40
Let o(h) = -h**3 + 5*h**2 - 4*h + 3. What is the least common multiple of 12/(3 - 1) - -1 and o(2)?
7
Suppose -v + 2 = 3. Let z = v + 10. Let k(y) = -y**2 - y + 11. Calculate the least common multiple of k(0) and z.
99
Let a(j) = 54*j**2 - j + 1. Let l be a(2). Let c = l - 503/2. Find the common denominator of 5/16 and c.
16
Let c be (15/14275)/((-6)/(-4)). Let g be -2 - ((-448199)/51390 + 0). Let h = g + c. Calculate the common denominator of h and 131/12.
36
Let j = -8 + 5. Suppose 5*w - 30 = -2*t - 3*t, 66 = 5*w - 4*t. Calculate the lowest common multiple of 4 - 3 - 15/j and w.
30
Suppose -3*u - 1 = -19. Suppose 2*p + 0*p = -u. Calculate the common denominator of p/3 - 266/(-36) and -53/12.
36
Suppose 4*z + i - 25 = -z, -2*z = 4*i + 8. Calculate the lowest common multiple of 10 and z.
30
What is the common denominator of 56/15 and -4 - (-3 - (-178)/36)?
90
Suppose 0*r - r = -5. Calculate the lowest common multiple of r and 5.
5
Let q(g) = -g**2 - 5*g + 10. Let k = 8 - 15. Let f be q(k). Calculate the lowest common multiple of 18 and (-3)/((-2)/f + -1).
18
Let y = 14/7251 - 776473/319044. Calculate the common denominator of y and 19/12.
132
Suppose 3*q = -5*k - 27, -79 = 6*q - q - 3*k. What is the common denominator of 1 + 6/(-99)*-48 and (q + 11)*32/30?
55
Let y(b) = -b**2 - 11*b + 5. What is the smallest common multiple of 3 and y(-11)?
15
Let y = -815 - -17927/22. Calculate the common denominator of y and 25/4.
44
Let k = -842/7 - -2139/14. Let z be (1238/10)/(12/10). Let p = z + -108. Calculate the common denominator of p and k.
6
Find the common denominator of 441/(-108)*76/14 and -74/9.
18
Let q = -1200 - -486. Let k = q - -2833/4. What is the common denominator of -31/3 