
171
Let t(i) = -i**2 + 35*i + 66. Let a be t(36). Find the common denominator of 63/40 and ((-162)/60)/9*94/a.
200
Let v(z) = z**2 - 147*z - 1706. What is the least common multiple of v(-11) and 288?
288
Let d = 27396 + -25748. What is the smallest common multiple of 56 and d?
11536
Suppose -c - 2*c = 1938. Let t = c + 5139/8. What is the common denominator of t and (-584)/14*21/336?
56
Let u(m) = 4*m**2 - m**2 + 2*m + 32 + 4*m - 4*m**2. Let d be -24*((-8)/12)/2. What is the least common multiple of 8 and u(d)?
16
Let p(y) = y**2 - 2*y + 3. Calculate the least common multiple of 38/4 - 160/(-320) and p(5).
90
Suppose -2*h = -5*m - 168, 2*m - 4 = -0. Let x = 107 - h. Calculate the smallest common multiple of x and 24.
72
Let f = -1220 + 386. What is the common denominator of -71/22 and (8 + f/57)/(0 + 20)?
2090
Suppose -3*q = -3*c - 12195, -20307 = -5*q - 0*c - c. Calculate the lowest common multiple of q and 4739.
28434
Suppose 3*s - 13 - 154 = 4*c, c = -5*s + 286. Let i be (-3 + (1 - 0))/(-2). What is the lowest common multiple of s and 3/((i/(-9))/(-1))?
513
Let p(h) = -5*h**3 - 64*h**2 + 18*h - 34. Calculate the smallest common multiple of p(-15) and 11.
23881
Let l = -529/429 - -8011/6006. Find the common denominator of l and 95/6.
546
Let y = -7600 + 114043/15. Let b = 52681 - 1264279/24. Calculate the common denominator of b and y.
120
Suppose 10*u - 9*u + 30 = 0. Let b be (6*1/(-8))/((-1)/(-4)). What is the common denominator of 49/4 and 6/b - 335/u?
12
Suppose -6 - 6 = 2*q - l, -q + 3*l = 1. Let n(t) = t**3 + 6*t**2 - 7*t + 12. Let v be n(q). Find the common denominator of 49/3 and 1/(-4) + (289/v - 5).
6
Let l = 2145243029/178710 - -553369/1554. Let x = -12360 + l. Let k = x + -423/230. Calculate the common denominator of k and 37/2.
10
Let h = -4/2155 - -5176/2155. Calculate the common denominator of h and -69/434.
2170
Let m = -46/1491 - 68533/178920. Find the common denominator of -71/20 and m.
360
Calculate the least common multiple of 16 and (-181 - 29)*(2 + 138/(-15)).
3024
Let j(d) be the third derivative of -7*d**4/24 + 63*d**3/2 + 13*d**2. Calculate the least common multiple of j(19) and 32.
224
Suppose -6 = -b - 2*u + 63, -4*u - 207 = -3*b. Calculate the least common multiple of b and 267.
6141
Let q(v) = -v**2 + 35*v - 57. Let y be q(33). Calculate the least common multiple of y*((-8)/(-14) + 5/(-21)) and 15.
15
Let f = -240084/74001235 + -6/41785. Find the common denominator of -11/644 and f.
7084
Let x = 77 + -236. Let u = 162 + x. What is the least common multiple of u and 12?
12
Suppose -6*c - 3*c + 38080 = 7*c. Calculate the smallest common multiple of c and 90.
21420
Calculate the common denominator of -55/48 and 81/(-360)*-10 + 4.
48
Let b = 31193/6 - 6685/3. Let d be ((-104)/42)/(-2)*2398. Let z = d - b. Calculate the common denominator of z and 41/22.
462
Let o = -167/4 + 43. What is the common denominator of ((-5)/15 + 9 + 1064/(-120))*-9 and o?
20
Let p = 4679 - 46697/10. Find the common denominator of p and (472/140)/(-18 - (-684)/30).
420
Find the common denominator of 89/7080 and (-17)/(-17) + (-296)/144.
21240
Let v(k) = 17*k + 10*k**2 + 5*k**3 - 4*k**3 + 31*k + 7*k**2 - 68*k + 16. Calculate the lowest common multiple of 16 and v(-18).
208
Let i be (-34)/4 - (-9)/(-18)*-1. Find the common denominator of 48/(-76) + (-2)/i + 1 and 79/2.
76
What is the common denominator of -27 - (27 + (-135643)/2510) and -143/6024?
30120
Find the common denominator of 3 - (5092/(-32))/19 and 63/2102.
8408
Suppose -3*x - 3*o - 249 = 0, -4*x - 2*o + 19 - 347 = 0. Let f = x + 91. Let a = 11 - 3. What is the lowest common multiple of a and f?
40
Let s(p) = p**3 - 2*p**2 - 5*p. Let g = -166 + 171. Calculate the smallest common multiple of s(g) and 10.
50
What is the common denominator of 94/1081 - (-8086)/(-76590) and -38/45?
1665
Let i = 49 - 58. Let x(l) = 5*l - 3. What is the least common multiple of 8/(-36) + (-56)/i and x(3)?
12
Suppose 2*g - 7 = v, -5*v + 31 = 5*g - 3*v. Let k(m) = m**3 - 5*m + 3. Suppose 0 = 2*r - 6*r. What is the smallest common multiple of k(r) and g?
15
Let i = 7681/42 + -371/2. Calculate the common denominator of ((-421)/(-1684))/((-15)/(-19)) and i.
420
Let v = -1313667/44 + 29856. Calculate the common denominator of v and 103/6576.
72336
Let f be (-54)/(-10323)*2/8. Let i = 41849/12617 + f. What is the common denominator of i and 139/6?
66
Let p = -39494/229 + 387345931/2246032. Find the common denominator of -31/14 and p.
68656
Let l(b) = -84*b - 208. Calculate the least common multiple of l(-6) and 8.
296
Let w(f) = -f**2 + 7*f - 5. Let s(q) = q**3 + 12*q**2 + 19*q - 2. Let o be s(-9). Let r = o + -69. What is the lowest common multiple of r and w(5)?
5
What is the common denominator of -48/31 and 2330/360 - 13 - -10?
1116
Suppose 4*l = 4, -2*a = -3*a + 5*l + 19. Let y = a + -11. Calculate the smallest common multiple of y and (-148)/814 + (-404)/(-44).
117
Let s = 21674 + -21640. What is the lowest common multiple of 1076 and s?
18292
Let t = 23336/7 - 1119577/336. Let o = -27/16 + t. Let r = o - 443/105. Find the common denominator of -82/33 and r.
165
Suppose 6*f = f + 22890. Let r = -17817/3010 - 2/215. Find the common denominator of r and (1/14)/(36/f).
84
Suppose -10*m + 131*m + 676 = 3096. Calculate the least common multiple of 120 and m.
120
Let f be (1 + -5)/(2 + 2712/(-930)). Let t = f + -9059/1278. Calculate the common denominator of -157/66 and t.
198
Suppose 5*r - 975 = 5*w - 0*r, -w = -4*r + 204. Let z = -2661/14 - w. Calculate the common denominator of z and -59/120.
840
Suppose n = 5 + 10. Let v be (n/(-18))/(4/(-24)). Suppose 0 = v*o - 2*s - 40, o + 5*s = 6*s + 8. What is the least common multiple of o and 5?
40
Let b(n) = -148*n**3 - 11 + 150*n**3 - 15 + 16*n**2 - 14 + 17 - 4*n. What is the smallest common multiple of 1239 and b(-8)?
3717
Let o be (-6 + 1 + 6)*-114823. Let s = -15615997/136 - o. What is the common denominator of s and 47/36?
1224
Suppose 1 = -l - m - m, -5*l = 5*m - 5. Suppose 6 = l*b + 6. Suppose -3*u + 109 = 5*v - 0*v, b = -2*v - 3*u + 49. What is the lowest common multiple of v and 6?
60
Let q = 2185 + -2148. What is the common denominator of q and -20/581?
581
Let x be 2/(-15) + (17742051/(-120))/9. Let h = x - -16422. What is the common denominator of h and -115/126?
504
Suppose 0 = 3*n + 5*n - 26848. Let w be (n/(-14))/(9/21). Let g = -11920/21 - w. What is the common denominator of -45/7 and g?
7
Let n = 75253/73320 + -5/3666. Calculate the common denominator of n and -12*(825/(-2000))/(1/2).
40
Suppose 5*k - 1160 = -3*k. Suppose 52 = 2*y + v, -2*v - k + 6 = -5*y. Calculate the smallest common multiple of 12 and y.
108
Suppose -5*z + 15 = 0, 3*b + b - 2*z - 26 = 0. Let m = -76 + 104. What is the least common multiple of m and b?
56
Suppose -2*j - 117 = -11*j. Let b(i) = -j*i + 6*i - 2*i - i**2. What is the lowest common multiple of b(-6) and 8?
72
Let y(b) = b**3 - b**2 - 22*b - 48. Let m be y(-9). Let j = m - -705. Calculate the least common multiple of j and 25.
225
Suppose -423*a = -241*a - 349622. Calculate the smallest common multiple of a and 18.
34578
Let z be (6 - (-102)/(-15))*35. What is the common denominator of (-87)/39*8/z and -109/78?
546
Let r(j) = 22*j + 244. Let i be r(-16). Calculate the common denominator of 14/4*64/36 and -3 + -1 + 6/(i/(-43)).
18
Let b(a) = -a - 4. Let k be b(-6). Let d be 3/(-12)*(-7925865)/155*k. Let l = d - 25568. Find the common denominator of -55/18 and l.
558
Suppose 104 = j - 13. What is the common denominator of (-4)/(-6) - ((-75)/j + 1) and 68/9?
117
Let o = -105791271/428 - -247176. Find the common denominator of (-6)/(-7) - (7658/588 + 1) and o.
1284
Let r = -277 + -451. Let c = r + 767. What is the least common multiple of c and 6?
78
Let l(h) = h**3 - 27*h**2 + 34*h - 193. What is the least common multiple of 1115 and l(26)?
3345
Suppose -f = 1, 0 = -0*g + 4*g + f - 755. Let b = -279/392 + -8/49. Calculate the common denominator of b and 2115/g + 2/14.
24
Let a = -21499/30 + 719. Calculate the common denominator of a and -181/30.
30
Suppose -585*u = -574*u - 44. Calculate the least common multiple of u and 2.
4
Let y(z) = -z**2 + 16*z + 36. Let p be y(18). Suppose c - 16 = -3*w + 2*w, 5*c - 25 = p. Calcu