
Suppose -90 = -37*p + 7*p. Suppose 0 = -p*s - 4*o + 284, 4*s + 8*o = 3*o + 379. What is the lowest common multiple of s and 18?
288
Suppose 8 = 6*w - 2*w. Let f(q) = -7*q + 68. Let y be f(10). What is the least common multiple of w and (732/90 - -8) + y/15?
16
Suppose -2*u - 3*v = 4, -5*v = 2*u + 2*u + 8. Let j be -1 + 2 + (u - (-2 - -1)). Suppose j = -3*t - 0*t + 33. Calculate the smallest common multiple of t and 4.
44
Suppose 0 = -u - 6578 - 12013. Let j be (2/(-36))/(517/u) + -2. Let z = 26615/4653 - j. What is the common denominator of -107/6 and z?
18
Let a(p) = -15*p + 99. Let z(c) = c**2 - 24*c + 69. Let v be z(21). Calculate the least common multiple of a(v) and 93.
279
Let q = -2772 - -282629/102. Calculate the common denominator of q and -8/2669.
16014
Let p = 144417/159800 - 172/1175. Find the common denominator of p and 84/44 + 1/(-2).
1496
Let o = -298951341/490 + 610105. What is the common denominator of o and 17/55?
5390
Let w(o) = 3*o**3 + 28*o**2 + 11*o + 20. Let u be w(-9). Calculate the smallest common multiple of 27 and u/((-15)/(-9)*7/35).
54
Let k = -113754 + 5009331/44. Let x = 13/11 - k. Let q = x + 90. What is the common denominator of q and -51/22?
44
Calculate the smallest common multiple of ((-9)/(-12))/((4 - 3)/4) and 1479.
1479
Suppose 0 = -4*x - 3*k + 1409 + 2376, 2*x - 1910 = 2*k. What is the common denominator of -1/16 and (270/x)/((-2)/15)?
304
Find the common denominator of -73/549 and (-17)/(-72)*40/(-150)*33.
5490
Let a(w) = 127*w + 27. Let f be a(4). What is the common denominator of (-10)/100*f/(-3) and ((-118)/(-16))/((-8)/16)?
12
Let v = -63994 - -11199002/175. Find the common denominator of v and -6/505.
17675
Let f = 286 - 283. Calculate the least common multiple of (-2544)/(-9) + 4/f and 2.
284
Suppose 25*z = 30*z - 295. Let f = -62 + z. What is the smallest common multiple of 6 and (1/f)/((-1)/18)?
6
Let t(h) = -h**3 - 26*h**2 - 4*h + 8. Let x = 399 + -390. Calculate the least common multiple of x and t(-26).
1008
Let z be 1565/4 + (-3 + 18)/(-5). Let s = z - 395. Calculate the common denominator of -2 + (2 - 170/8) and s.
4
Find the common denominator of (1/14)/(0 + (-4)/113) and ((-6)/4 - -1)/((-748)/(-1479)).
616
Suppose -6*w = -152 + 62. Suppose -160 = -19*a + w*a. Calculate the least common multiple of 2 and a.
40
Let s(z) = -z**2 + 21*z**3 - 7*z**3 + 17*z**2 + 27*z - 13 - 13*z**3. What is the smallest common multiple of 10 and s(-14)?
10
Suppose -59*d + 33054 = -4116. Calculate the smallest common multiple of 126 and d.
630
Calculate the common denominator of ((-13 - -3)/2)/(7788/(-275)) and -31/14.
4956
Find the common denominator of 3/(-5) + 740/(-300) and (-11 - -12)/(9/(-37)) - 2.
45
Let f(u) = 7*u**2 + 10*u + 2. Let w be f(-3). Suppose 8*z - w = -3. What is the least common multiple of z and 54?
108
Let k(x) = 11*x - 2. Calculate the least common multiple of (-195)/(-12) - (-18)/(-72) and k(2).
80
Let j = -12369 + 61887/5. Calculate the common denominator of -39/343 and j.
1715
Let f(h) = -8*h + 70. Let q be (1 + -3)/(6/72*-4). Calculate the least common multiple of (-2)/(-5) - (-304)/40 and f(q).
88
Suppose 6*a = -180 - 1200. Let k = 252 + a. What is the smallest common multiple of k and 18?
198
Let b = -415/6 - -1084/15. Find the common denominator of (12/21)/(-2) + (-293)/(-756) and b.
540
Let i(b) = 49 - 25 + 5*b - 24. Calculate the smallest common multiple of i(3) and 5.
15
Let h = 933590/82473 - -70/2229. Let f = -1761/148 - h. Let s = 12928/11 - 76721/66. Calculate the common denominator of f and s.
12
Suppose 0 = 4*s - 3 + 7, g + s = 2. Suppose 0 = -t - 3*t + 92. Suppose 9*p = t + 31. What is the lowest common multiple of p and g?
6
Calculate the common denominator of (3/(-566))/(333/2257) and 47/1415.
8490
Suppose -7*k - 56 = -21*k. Let l = 84 + -40. What is the smallest common multiple of -2 - (-4 - 38*(k + -3)) and l?
440
Let n = 60755/12 + -5069. Let v = 61727/26642 - 366/173. Calculate the common denominator of v and n.
924
Let q be 0/5*(-3)/6 - 45. Let u = q + 39. Calculate the lowest common multiple of 1 and (-22)/33 - 16/u.
2
Calculate the common denominator of (2457/(-288) + 19)*2/110 and -38/1133.
36256
Let n = 861601/819978 + -14/8039. Find the common denominator of 95/24 and n.
408
Let r = 11/4 + 59/36. Let a = 6658 + -4494. Find the common denominator of r and a/(-360) - 2/(-5).
18
Let f = -1933439/9657 - -7402/37. What is the common denominator of -67/261 and f?
261
Calculate the common denominator of 7 - (-5 - (-140)/30)*(-174)/(-16) and -5/814.
3256
Calculate the common denominator of 108/1998 - (-7626)/(-19240) and -53/234.
2340
Let t = 81 - 36. Let v = -41 + t. Let s = 8 + v. What is the lowest common multiple of 20 and s?
60
Suppose -5*l - 3 = -18. Suppose -c - 1 = -l. Calculate the smallest common multiple of c and 168/132*3 + (-14)/(-77).
4
Suppose -4*t = 4*p + 13292, 3*t - 5*p - 6294 + 16271 = 0. What is the common denominator of -21 and (-3)/7 - t/4032?
48
Let p be 148/8 - 2/4. Let y(b) = -b**3 - 4*b**2 + 2*b + 13. Let z be y(-2). Calculate the common denominator of 67/27 and (7/z)/(p/33).
54
Let d = 9358087259/61 - 153420963. Let x = d + 9697. Calculate the common denominator of -19/11 and x.
671
Let o = -10508 - -10510. Calculate the smallest common multiple of 8584 and o.
8584
Suppose -77 = -a - 2*z, -4*z - 464 = -5*a - 93. Let i(v) = v**2 - 10*v - 16. Let b be i(0). What is the smallest common multiple of 10 and (b/(-10))/(10/a)?
60
What is the lowest common multiple of (-600)/(-36)*51/(-2)*-4 and 14?
11900
Suppose -5*v - 29 = -3*c, -2*c + 19 = -v - 5. Let r = c + -9. Suppose r*p - 79 = 9. What is the least common multiple of p and 10?
110
Suppose 25 = -2*r + 69. Suppose 65*a - 1 = 64*a. What is the smallest common multiple of (-2 + a - -3)/((-5)/(-20)) and r?
88
Let t = -37339/10 + 3728. Suppose -2*v - 2*d = -16690, v - 5*v + 2*d + 33362 = 0. Let c = v + -166769/20. What is the common denominator of c and t?
20
What is the common denominator of ((-42)/(-224))/(50/848*6) and 1/300?
300
Let p = -13659 - -13719. Calculate the smallest common multiple of 1800 and p.
1800
Let u(l) = -14*l - 132. Let i(b) = -b**2 + 7*b + 1. What is the least common multiple of u(-17) and i(6)?
742
Let m be -1*(-3 + -4) + 4. Suppose -7*o + m + 17 = 0. Suppose 3*y - 2*y = 5*j + 19, -4*j + 20 = 0. Calculate the least common multiple of o and y.
44
Let r = 221 + -146. Calculate the common denominator of (-2)/(-4) - 1/((-6)/r) and -23/39.
39
Let o(s) = s**2 + 6*s. Let n be o(-11). Suppose 59*q = n*q - 20. Let p(b) = b**3 + 7*b**2 + 3*b - 5. Calculate the least common multiple of 15 and p(q).
30
Let n = -98 - -56. Find the common denominator of (-2)/(-2) - 82/24 and (7/(-3))/((-32)/n).
48
Let p(a) be the first derivative of -a**4/4 + 11*a**3/3 - 19*a**2/2 - 8*a + 25. Calculate the least common multiple of p(8) and ((-8)/6)/(14/21) - -42.
160
Let y = 2209/2 + -1088. What is the common denominator of y and (1 + (-7)/6)*1254/(-1444)?
76
What is the common denominator of ((-5)/(-3))/(-5) + 1682/(-435) and 3/4*(-492)/(-18)?
10
Suppose -4 = t - 2, -5*l + t = 8. Let f be 52100/(-525) + 0 + l. Let y = f + 625/6. Find the common denominator of y and -35/6.
42
Suppose -4*p - 2*o - 3*o - 12266 = 0, -2*p + 2*o - 6124 = 0. Let v = p - -30579/10. Calculate the common denominator of -17/12 and v.
60
Suppose -5*p + 3*r - 105 = -0*r, 0 = -5*p - r - 125. Let l = 499 + -1001/2. What is the common denominator of ((-279)/p)/3 + -1 and l?
8
Let f = -66 + 70. Let s be -2*((-4)/f)/2 - -3. Calculate the common denominator of 18/(-6) - (-70)/s - 1 and 31/2.
2
Let o(d) = -d**3 + 10*d**2 - 8*d - 8. Suppose -20*i - 14 = -22*i. Let a be o(i). Let q = a + -78. Calculate the lowest common multiple of 7 and q.
35
What is the common denominator of 83/816 and (-1464)/(-1989) + (-330)/715?
816
Let b be 10*(39/(-15) + (2 - 0)). What is the lowest common multiple of b*8/(-12) - -4 and 18?
72
Suppose -25*s + 1488 = -21*s. Suppose -2*c - 370 - 2 = 2*q, -3*c = 2*q + s. What is the common denominator of q/36*1/3 and 11/3?
18
Let a = -13714 + 329207/24. Let d = 6/1960945 + 135154212037/64711185. Let l = d - 2090. What is the common denominator of l and a?
264
Let f be 1/(-7)*2 - (-32)/14. Let p be -6*1*(-3 - 9). Supp