70
Let p(f) = f**2 - f + 2. Let l be p(-3). Let b = 6 + l. Calculate the common denominator of -109/44 and (-5)/(-12)*(-188)/b.
132
Let h = 1929/6886 - 45/313. What is the common denominator of h and (15/18)/(2/(-23))?
132
Let s(l) = -10*l**3 - 4*l**2 - l + 2. Calculate the least common multiple of s(-1) and 90.
90
Let k = 43/7 + -113/56. What is the common denominator of -10/7 and k?
56
Let j(r) = 3*r - 44. Let k be j(13). What is the common denominator of -77/6 and (-38)/(-6) - (k - -3)?
6
Let f = -919 - -928. Let h = 4 - -7. What is the smallest common multiple of f and h?
99
Let s = -464 + 1821/4. Let a = 3131/8 - 393. What is the common denominator of a and s?
8
Suppose 195 = 13*u - 234. Calculate the least common multiple of u and 129.
1419
Let y(w) = -12*w - 81. What is the lowest common multiple of y(-22) and 27?
1647
Let c be 4/1*(-1 + 2). Suppose -43*t + 50 = -38*t. Let f = c + t. Calculate the lowest common multiple of f and 2.
14
Let l = 123 - -87. Suppose -66 + l = q. What is the smallest common multiple of 22 and q?
1584
Let l = 486181/228229 - -2/9923. Calculate the common denominator of 3/2 and l.
46
What is the common denominator of -31/3 and ((-2475)/300)/((-18)/(-13))?
24
Let h = -150 - 68. Let f = 4104 + -8669/2. Let c = h - f. Calculate the common denominator of -13/4 and c.
4
What is the common denominator of -26/29 and ((-8)/(-16))/(20/328)?
145
Let h(s) = -s**3 - 25*s**2 + 28*s + 97. Calculate the smallest common multiple of 48 and h(-26).
720
Let h be 62/(-14) + 2 - (-12)/(-21). What is the common denominator of (6/32)/((-120)/35 - h) and 23/10?
80
Suppose 4*r = 5*y - 21, -1 = 5*y - 6. What is the smallest common multiple of 18 and (9 - -3) + r - -2?
90
Suppose -2*m = -5*z + 16, 2*z - 3*m = 5*z + 3. Calculate the common denominator of 2325/540 - 1/z and -3/20.
180
Suppose 5*a - 153 = -128. What is the least common multiple of 33 and a?
165
Suppose 4*t + 31 = 7*t + 2*r, 2*t - 14 = 2*r. What is the smallest common multiple of t and 69?
207
What is the common denominator of (-8)/176*(-246)/(-12) and 67/8?
88
Let z = -12 - -30. Let s(l) = -l**2 - 26*l - 38. Calculate the least common multiple of z and s(-2).
90
Suppose 2*c + 214 = 2*i, 4*i - 388 = -0*i - 4*c. Find the common denominator of (-134)/132 + 1 + (-68)/i and 39/16.
176
Suppose 4*r = 4*k - 136, k + 5*r - 103 = -k. Let h = k - 29. Calculate the smallest common multiple of 4 and h.
20
Suppose 72 = 5*p + 13*p. Let j(b) = -b**2 - 8*b - 9. Let g be j(-6). Suppose -55 = -2*k - g*k. Calculate the least common multiple of p and k.
44
Suppose -5*b + 7 = r - 5*r, 4*r + b = 11. Let p(l) = -l**3 + 5*l**2 + 3*l - 12. What is the least common multiple of r and p(5)?
6
Let u = 2016 - 82661/41. Find the common denominator of u and 41/3.
123
Let p = 6472/7 + -39791/42. Find the common denominator of p and 23/180.
180
Let i(p) = 3*p - 10. Suppose 4*s - 8 = 2*s. Let y be i(s). Let t(x) = 10*x - 4. Calculate the smallest common multiple of 12 and t(y).
48
Let n = -979 + 1012. Suppose -3*r - 4*h = -33, 30 = 2*r - 3*h - 9. What is the lowest common multiple of n and r?
165
Suppose 25*g - 36 = 22*g. Let m(z) = -z**3 + 12*z**2 + z - 4. Calculate the least common multiple of 11 and m(g).
88
Calculate the least common multiple of 6 and (-147)/(-14)*(-2)/(-3).
42
Let w be (-64)/350 + 2/7. Let b be 1 + 5 + (-82970)/(-7000). Let k = b - w. Calculate the common denominator of k and 11/16.
16
Let i(j) = j**3 - 29*j**2 + 214*j - 36. What is the lowest common multiple of 18 and i(16)?
180
What is the common denominator of 0/(-39) - (189/(-5))/(-3) and -44/9?
45
Let j = 6856 + -75661/11. Let a = 1867/110 + j. Calculate the common denominator of a and -131/12.
60
Suppose 16*h = 2*h + 2772. Suppose 0 = 14*a - 3*a - h. What is the smallest common multiple of a and 33?
198
Suppose 164 - 32 = 11*p. What is the lowest common multiple of p and 32?
96
Let d = -8123237716/157945 + 257154/5. Let r = -2685109/694958 - d. Calculate the common denominator of r and -89/26.
286
Let z(k) = k**3 + 9*k**2 + 7*k - 7. Let t be z(-8). Suppose a - 11 + t = 0. What is the smallest common multiple of 5 + (2 - 0) - 1 and a?
30
Find the common denominator of 1/2 - (1 + (-792)/2128) and 103/28.
532
Let y be (2/(-6))/((-1)/(-3)). Let t = 15 + y. Let d(z) = z**2 + 4. What is the smallest common multiple of t and d(-4)?
140
Let v be -167 - -2*(-2)/4. Calculate the common denominator of -20/7 and (9/10)/(18/v).
35
Let f = 31 + -27. Suppose 5*l + 7 = f*l. What is the common denominator of 367/(-14) + 2/l and -143/18?
18
Let n = -10078767/767 - -26281/2. What is the common denominator of n and 15/16?
12272
Suppose -r - 15 = 2*r, -3*u + 3*r = -69. Suppose 3*n - 4*h - u = 0, -h + 1 = -4*n + 12. Calculate the lowest common multiple of 14/(n/1) - -3 and 16.
80
Let d(w) = w**3 + 6*w - 38*w**2 + 19*w**2 - 12 + 15*w**2 - 2. Calculate the smallest common multiple of 12 and d(4).
60
Let j be 171 - (-1 - (-1 + 0)). Let x = -109 + j. Suppose 2*d = -2*a + 4*d + 38, -3*a + 4*d + x = 0. Calculate the smallest common multiple of 16 and a.
112
Suppose -3*x = -2*b - 0*b + 7069, -2*x + 14178 = 4*b. Calculate the common denominator of (b/(-40))/(-11) + -2 and 3/8.
40
Let q = -6637 + 146109/22. Find the common denominator of q and (27/(-2))/9 - 4.
22
Suppose 344 = 5*m - 1411. Let t = 1435/4 - m. What is the common denominator of -21/34 and t?
68
Calculate the common denominator of -12/41 and (-3)/((-36)/(-236))*1/(-3).
369
Let k = 10256/615 + -2/205. Calculate the common denominator of k and -25/108.
108
Let f(v) = 8*v + 2. Let r be f(2). What is the common denominator of 25/14 and (13/r)/(14/105)?
84
Let j = -32 - -54. Let v(q) = 18*q**2 + q + 1. Let h be v(-2). Suppose -h = -3*t + 5*z, -5*t + 92 = -t - 4*z. Calculate the smallest common multiple of j and t.
22
Let r = -6167/2196 + 214/183. Calculate the common denominator of 137/30 and r.
180
Calculate the least common multiple of 45 and 5/(-2)*2 - (-5986)/146.
180
Let w = -389/2 - -186. Suppose 5*s + 15732 = 4*a, 4*a - 3*s - 14521 - 1203 = 0. Let l = a + -78541/20. Find the common denominator of w and l.
20
Let x = -383641/7 + 55174. Let b = x + -369. Calculate the common denominator of -54/7 and b.
7
Let o = -2568846/11 - -232723. Let s = -810 - o. Let h = 8345/6 - 1401. What is the common denominator of s and h?
66
Suppose 5*p - 17 = -4*v + 11, 0 = -3*v - 3*p + 24. Let b(z) = 66*z - 978. What is the smallest common multiple of b(15) and v?
12
Let m = 21 + -14. Let y = m + -4. What is the smallest common multiple of ((-9)/(-36))/(((-10)/8)/(-5)) and y?
3
Suppose -2*m - 26 = -4*a, 2*m - 22 = -2*a - 0*a. Let u(l) = 0*l**2 + 12*l - l**3 - 13 + 4 - 12*l**2. Calculate the lowest common multiple of a and u(-13).
8
Suppose 0 = 5*k - 178 - 647. Let l = k + -99. Find the common denominator of l/(-40) + 1/4 and -43/9.
45
Let t(d) be the third derivative of d**5/30 + 23*d**4/24 - d**3/2 + d**2 + 8. What is the least common multiple of t(-12) and 10?
90
Let b = -887/3 - -308. Calculate the common denominator of b and (-40 + 1)*17/187.
33
Let y = -58 + 61. Suppose -r = 3*x - y, -32 = -5*r + 3*x + 1. What is the smallest common multiple of 56 and r?
168
Let i(v) = v**2 + 5*v + 18. Let c be i(-8). Let t = c - 26. What is the smallest common multiple of 20 and t?
80
Let b be ((-21021)/2175)/(24/30). Let i = 520/29 + b. What is the common denominator of -61/10 and i?
20
Suppose -2*v + 51 = 21. Let c = 2 + v. Calculate the smallest common multiple of c and 5.
85
Suppose 0 = -3*h - 15, 5*t - 272 = 4*h - 12. Calculate the common denominator of t and 73/470.
470
Find the common denominator of 1768/1365*(-15)/(-10) and 1/5.
35
Let u = 138 - 132. What is the least common multiple of 15 and u?
30
Let n(j) = 3*j + 12. Calculate the lowest common multiple of n(-2) and 321.
642
Let c = -894 + 896. Calculate the least common multiple of c and 10.
10
Let a = -12 - -16. Let j = 7 - a. What is the least common multiple of j and 7?
21
Calculate the common denominator of (-615)/(-2430) - 10/12 and 40/9.
81
Suppose -n - 2 = 0, 4*b - 26 = -n + 4*n. Suppose l - 4 = 3*w - 8, 2*l - 14 = -b*w. Suppose 6*r - 20 = l*r. Calculate the smallest common multiple of 9 and r.
45
What is the common denominator of -101/88 and (-44)/(-66)*5