8.
2016
Find the common denominator of (9/30 - 42/540)/(1256/762) and 145/942.
942
Suppose a + 3635 = -3*o, 5*a + 3*o = -2450 - 15677. Let g = a + 79729/22. Let v = 44453/8024 + 5/3009. Find the common denominator of g and v.
264
Let q(w) = 2*w**2 + 5*w - 351. Calculate the least common multiple of 102 and q(-15).
408
Suppose 26 = -3*i + 35. Suppose -9*v + 14*v = 10, 0 = y - i*v - 7. What is the smallest common multiple of y and 143?
143
Let k(d) = 2*d + 16. Let m be k(-6). Suppose x + 3*p = m*x - 6735, 4*x + p = 8975. Calculate the common denominator of 78/x + 2/(-11) and -65/12.
204
Let a = 2895 + -60776/21. Let c = -22 - -23. What is the common denominator of a and ((507/(-54))/13)/(c/11)?
126
Suppose 0 = -80*v - 49*v - 35*v + 120*v + 352. Let r = 9 + 29. Calculate the least common multiple of v and r.
152
Let f be 0*-2*(-5)/30*-3. Suppose 5*a - 12*l = -10*l + 156, f = 2*a + l - 66. Calculate the smallest common multiple of 10 and a.
160
Let d = -67443 + 6204681/92. Let s = -6031/2 - -3052. What is the common denominator of s and d?
92
Let j be (54/15)/(-6)*10. Let a be (27912/(-36))/(j/(-243)). Let q = a + 941917/30. Calculate the common denominator of q and 1/3.
30
Let w(o) = -12*o**2 - 2*o. Let r be w(-1). Calculate the common denominator of (-7)/168*r*(2 - 1) and -41/294.
588
Calculate the lowest common multiple of ((-155)/20 + 2 - 24/(-32)) + 129 and 260.
8060
Let s be -13*(2 + -3 + 0). Let q(o) = -o**3 + 12*o**2 + 11*o + 14. Let k be q(s). Let j = k - -22. What is the smallest common multiple of j and 4?
20
Let f(p) = -134*p - 22. Let o be f(-6). Suppose o = 4*b - 4714. Find the common denominator of 2/6 - b/(-468) and -58/3.
78
Suppose 537*c - 2*a = 542*c - 160, 3*a = -5*c + 160. Suppose 36 = 5*j - v, 2*j + 4*v - 12 - 20 = 0. Calculate the least common multiple of j and c.
32
Let k(f) = -3*f**3 - 25*f**2 - f + 2673. What is the lowest common multiple of k(0) and 972?
10692
Suppose -100*y = -99*y - 63. Find the common denominator of 574/(-180) + 14/y and -79/66.
330
Suppose -106 = -26*p + 440 - 0. What is the smallest common multiple of p and 7 - -2*(-2)/(-4)?
168
Let t(x) = 3*x - 15. Let b be t(0). Let m be 27/5 - (-6)/b. Calculate the smallest common multiple of 38 and (m/((-15)/(-4)))/((-12)/(-9)).
38
Let w be (-3)/(-9) - (-440750)/75. Let o = -233699 - -2395841/10. Let v = o - w. What is the common denominator of v and -27/22?
110
Let p = -6 + 12. Let f(d) = -38*d - 6. Let i be f(2). Let s = 98 + i. Calculate the smallest common multiple of s and p.
48
Let s(p) = -p**2 - 69*p + 1548. What is the lowest common multiple of 36 and s(-69)?
1548
Let k = 2609 - 1085343/416. Let a = k + 363/416. Calculate the common denominator of a and (-57)/(-2)*10/18.
24
Calculate the common denominator of -89/8 and -34*(-2 - -1 - 1)/(-1 - -315).
1256
Suppose 0 = b + 4*n - 23, 0 = 2*b + 97*n - 102*n + 6. What is the smallest common multiple of 258 and b?
1806
Suppose 26 = 2*p + 4*w, p = 5*p - 2*w - 12. Suppose p*q - 171 = -4*q. Suppose -3 = 5*a + 2, 2*b + 2*a = 0. Calculate the lowest common multiple of b and q.
19
Let p(t) = 3*t**2 - 2. Let w be (-51)/36*2 + 2/(-12). Let s be (w - -5) + -4 + 0. What is the lowest common multiple of p(s) and 40?
40
Let k = -72 - -66. Find the common denominator of 154/(-36) + -2 - -4 and (5 - -4) + k - (-38)/(-4).
18
Suppose 0 = 4*y - 0*h - 4*h - 84, 5*y - h = 125. Suppose y*k - 8847 + 2217 = 0. What is the least common multiple of 12 and k?
1020
Suppose 0 = -187*j - 59*j + 103320. What is the least common multiple of j and 45?
1260
Let f be (4 - 3481/210) + (-21)/(-35). Let u = 12 + f. Find the common denominator of -121/18 and u.
126
Suppose -p + 60 = p. Let o = -85 + p. What is the lowest common multiple of (o/(-15) - 4) + (-55)/(-3) and 22?
198
Calculate the common denominator of 19/1224 and 2/(-40)*43/((-817)/(-2622)).
6120
Suppose w + 286 = -c + 3*c, -4*c + w = -568. Suppose 83*z - 81*z - 3*y - c = 0, 2*y + 347 = 5*z. What is the least common multiple of z and 15?
345
Let b = 1101229/720 - 26941/80. Let a = 1187 - b. Find the common denominator of a and 83/262.
2358
Let v = -17004 - -476229/28. Let b = -677/4 - -4797/28. Let c = b + v. What is the common denominator of -43/8 and c?
8
Let q = 7491037/15882 + -9/5294. Let f = q + -3001/6. What is the common denominator of f and (1 - 1) + 54/(-8)?
4
Suppose -4*d = 132*k - 136*k + 4728, -2*k = -5*d - 2382. Calculate the smallest common multiple of k and 140.
5880
Suppose -3878 = 2*p - 3918. What is the least common multiple of 18 and p?
180
Let o be ((-120)/21)/(2/(-7)). Suppose 3*y - o = -2*y. Suppose y*b - 94 = 50. What is the smallest common multiple of 6 and b?
36
Suppose 0 = -8*t + 4 + 20. Let c(m) = m**2 + 8*m - 7. What is the smallest common multiple of t and c(-14)?
231
Let f = -1914 + 19191/10. Let y = 18319 + -494605/27. Calculate the common denominator of y and f.
270
Let d = 13800 - 21381. Let f = -166729/22 - d. Calculate the common denominator of 4/(-10) - (-1834)/(-840) and f.
132
What is the common denominator of -2/1253 and (-2 - 815/(-10))/((-495)/(-30))?
13783
Suppose 0 = -34*o + 43*o - 4158. Let y = -408 + o. Calculate the least common multiple of y and 27.
54
Find the common denominator of 5 + (138360/(-5412))/5 and 35/697.
7667
Suppose 394 = 2*o - 5*i, 0 = 43*o - 48*o + 5*i + 970. Calculate the smallest common multiple of o and 1584.
6336
Let q = 1721/9 - 334009/1746. Calculate the common denominator of -1/76 and q.
7372
Let p be (-3998323)/1911 - ((-16)/6)/(-4). Let r = p + 2093. Find the common denominator of r and -55/14.
182
Let i = -444 + 784. Calculate the common denominator of -62/35 and 629/i*4/(-5).
175
Let z = -2337241/12 - -192505. Let h = 2262 + z. Let q = 2451/2 - 34273/28. What is the common denominator of h and q?
84
Let q = -125447/33 - -3801. Calculate the common denominator of 20/(-138)*75/30 and q.
759
Suppose 3*y + 2*y - 13 = 3*t, -4*y = -4*t - 20. Let a be (2 + -9 - t)*(-6)/(-398). Let i = 8761/13532 + a. Calculate the common denominator of 23/6 and i.
204
Let f = 32/123 + -43975/246. Let k(s) = -25*s**3 - 4*s**2 + 4. Let o be k(-2). Let p = f + o. What is the common denominator of p and 89/8?
8
Let w(l) = 21*l**2 + 881*l + 30. What is the smallest common multiple of w(-42) and 10?
360
Suppose 2*n + 0*n + 16 = 2*c, 0 = -4*n + 2*c - 32. Find the common denominator of n/(-28) - (-292)/(-3080) and 19/20.
220
Suppose 91*y - 94*y = -17991. Let q = y + -36085/6. Calculate the common denominator of q and 107/12.
12
Let d be (-38)/74*(-543)/(-6). Let j = d + -1/37. What is the common denominator of (16 - 7)*31/(-42) and j?
14
Let s(u) = u**3 + 47*u**2 + 88*u - 40. Let w(j) = -3*j - 108. Let i be w(-21). What is the smallest common multiple of s(i) and 20?
100
Let w(f) = -f**2 + 31*f - 43. Let v be w(29). What is the least common multiple of 42/10*50/v and 158?
1106
Let r be (0/5)/(-4) + (-32)/(-2). Let j be r/(-10)*(0 - -5). Let d = j - -22. Calculate the lowest common multiple of d and 20.
140
Let y(l) = -l**2 - 29*l + 182. Let w be y(20). Let r = 897 + w. Calculate the smallest common multiple of r and 18.
198
Let v = -129943/18 - -7214. What is the common denominator of 17/807 and v?
4842
Let a = 19/444 + 225/74. Find the common denominator of -59/564 and a.
564
Suppose -3*z - 5*s + 65 = 30, 2*s = 5*z - 17. Suppose -z*u + 4978 = 4*k, 4*k + 2008 = -18*u + 20*u. Calculate the least common multiple of 8 and u.
3992
Let s be (2 + -1)*(7 + -16)*-3. Suppose -s*t - 986 = -3362. What is the lowest common multiple of t and 44?
88
Let s = -47 + 49. Suppose -s*k + 144 = 436. What is the common denominator of k/72 + (-48)/(-12) and -27/11?
396
Let j = -4419 - -2951891/668. Find the common denominator of j and -50/501.
2004
Let i(w) = w**2 + 44*w - 1754. What is the smallest common multiple of i(-82) and 87?
39498
Calculate the lowest common multiple of 13 and ((-12331)/(-177)*(4 + 5))/((-6)/(-14)).
19019
Suppose -35*a + 51*a - 64 = 0. Find the common denominator of (-2)/a - 76/504 and -101/24.
504
Let a be 5508351/1101672 - 15/3. Let w = a + 1965627669/612040. Let o = 3201 - w. Calculate the common denominator of -21/10 and o.
10
Let d = -20 - -17. Let u(j) = 263*j**2 - j - 4. Let h be u(d). Let m = -9383/4 + h. Calculate the common de