 i. What is the smallest common multiple of 4 and 42/t - (-5 - -3)?
16
Let f(u) = 5*u + 45. Suppose 17*o - 16*o = -3*g + 47, 5*o = 3*g - 17. What is the least common multiple of f(-2) and g?
70
Suppose 2 = 3*n + 2*y - 11, 3*y = -4*n + 17. Suppose 7*m - 3*p - 132 = 3*m, -n*m = -5*p - 160. What is the lowest common multiple of m and 14?
252
Find the common denominator of 74/105 and (-300)/(-800) - 103/1800.
3150
Suppose -144 = -5*f + s, 5*f - 4*s - 112 = f. Let b = -20 + f. Suppose 0 = b*r + 16 + 29. Calculate the common denominator of -1/13 and r.
13
Let t = 52554 + -2522689/48. What is the common denominator of -1/224 and t?
672
Suppose 4 = 2*q - 0. Suppose -q = 3*w + 7. Calculate the smallest common multiple of (-5 - w) + 4 - -31 and 15.
165
Let h = 70033 + -766846/11. Let l = h - 321. Calculate the common denominator of 115/28 and l.
308
Let v(u) = 5*u - 3. Suppose -6 = -5*x - 2*k, 4*x - 4*k + 2*k - 12 = 0. Let i(n) = 2*n**2 - n - 9. What is the least common multiple of v(x) and i(3)?
42
Let r = -17925 - -20179. What is the lowest common multiple of 140 and r?
22540
Let i = 8309491 + -7520087819/905. Let y = -1/362 - i. What is the common denominator of y and 119/18?
90
Let p = -47807/683000 - -28/683. What is the common denominator of p and 63/2?
1000
Suppose -6*j + 211 = -5*j - 4*i, 0 = 4*i + 4. Let d = j - 141. Calculate the smallest common multiple of d and 66.
66
Let i = -588 + 237. Calculate the least common multiple of i/(-108) - (-1)/(-4) and 18.
18
Let d = -2077/2040 - -7/136. Let t = -15547/20 - -781. Find the common denominator of d and t.
60
Let h(q) = 8*q**2 + 17*q - 75. Suppose 1124 - 1128 = -o. Calculate the least common multiple of h(o) and 55.
605
Suppose k = -2*k - 50259. Let j be (k/(-16))/1*24/(-18). Let s = -1388 - j. Find the common denominator of s and 7/30.
60
Let o = 2224687/5146560 - -2/80415. What is the common denominator of 1 - 1*(-134)/(-8) and o?
192
Let v = 16 - 42. Let w = 92 + v. What is the least common multiple of 72 and w?
792
Let i = -114 + 182. What is the common denominator of 45 and 2/4 + ((-114)/i)/(-19)?
17
Suppose -3*t = 2*s - 562 - 817, -449 = -t + 2*s. Suppose -3*z = -5*v - t, -v = z - 0*z - 163. What is the least common multiple of z and 27?
1431
Let g be ((-1)/(38/172))/(1535172/(-18)). Let l = g - -89600440990/38582326497. Let y = l + 49/481. Calculate the common denominator of y and 71/24.
264
Suppose 5*m - 45 = -2*u - 19, 0 = m + 2*u - 10. Suppose -2*y = 3*r + 5, r = m*y + 11 + 6. Calculate the lowest common multiple of r and 77.
77
Suppose -4 + 31 = a. Suppose 3*s - p - 56 = 0, -105*s + 104*s + 4*p - 7 = 0. Calculate the lowest common multiple of a and s.
189
Let w = 439836 - 775870679/1764. What is the common denominator of 125/84 and w?
1764
Let d = 1361/102 + -7704/595. Find the common denominator of d and -25/42.
210
Let u(v) = -2*v**2 - 21*v - 37. Let x(k) = -3*k**2 - 31*k - 55. Let i(m) = 7*u(m) - 5*x(m). Calculate the smallest common multiple of i(-8) and 80.
80
Let b = -20 + 24. Suppose 33 = a + 2*a + j, -b*j + 24 = 3*a. What is the lowest common multiple of a and ((-44)/(-11))/(8/52)?
156
Let o = -23712 - -2062969/87. Let w = 13151/2690 - -1/24210. Calculate the common denominator of o and w.
261
Let k = -8147/2 - -4024. Let l be 6/18 - 1573/12. Let v = l + 141. Find the common denominator of v and k.
4
Suppose 2*i = 5*l - 354, -2*l + 2*i + 153 = 5*i. Calculate the lowest common multiple of l and 72.
72
Suppose 149*d = 155*d - 132. Calculate the least common multiple of d and 38.
418
Suppose -20*d = -19*d + 1, 5*a + 3*d - 207 = 0. Calculate the least common multiple of 2751 and a.
5502
Let k(v) = v - 10. Let l be k(12). Suppose f - 499 = -5*d, 0 = -d + l*f - f + 95. Calculate the common denominator of -50/9 and (-278)/(-36) - 11/d.
18
Let q be (-1428)/(-85) - (-8)/(-10). Suppose 0 = q*k - 9*k - 147. Calculate the common denominator of 61/10 and k.
10
Let t = -6395 + 14229. Let m = 117464/15 - t. What is the common denominator of -86*(45/22 + -2) and m?
165
Let q(i) = i**2 + 9*i. Let w be q(-14). Suppose 3*k = -4*k + w. What is the least common multiple of 44 and k?
220
Let m = -312681885/1588 + 196903. Find the common denominator of 137/2382 and m.
4764
Suppose 18*h - 15*h - 171 = 0. Let p = -68177/10 - -6824. Calculate the common denominator of (-19)/(h/44) - (4 + 0) and p.
30
Let t be 7 - (-1 - 91315/(-1386)). Let c = t - -529/9. Calculate the common denominator of c and -123/10.
330
Suppose p = -o + 11, -10*o + 7*o + 2*p + 23 = 0. Calculate the lowest common multiple of 1320 and o.
3960
Suppose -4*v + 2*y + 26644 = 0, -v + 6674 = -y + 13. What is the least common multiple of v and 1?
6661
Find the common denominator of -81/292 and (2 + 78/(-36))/(28/707).
1752
Let i(c) = c**2 + 71*c + 88. Let w be i(-46). Calculate the common denominator of 10/13 and (-112)/(-504) + (-268)/w.
767
Suppose -13*g + 53 = -51. Suppose 412 = 14*i - g. What is the lowest common multiple of 15 and i?
30
Suppose 0 = -3*p - 3*u + 18, -5*p + 36 = 3*u + 10. Suppose 5*j + d - 748 = 0, 5*d = p*d - 2. What is the least common multiple of j and 165?
1650
Calculate the common denominator of (-33369)/1512 + 21 - 2/(-8) and 49/80.
720
Let k(b) = b**3 - 47*b**2 + 556*b - 42. What is the lowest common multiple of 126 and k(25)?
756
Let b = 132 + -43. Let n = -980/11 + b. Find the common denominator of n and 41/6.
66
What is the least common multiple of 504 and (33/88 + 146/(-48))*(-9)/3?
504
What is the lowest common multiple of 12 and 8 - (55/(-20))/(-11)*(-1 - -1)?
24
Let s(q) = 25*q**2 + 85*q + 279. Calculate the lowest common multiple of 1115 and s(-6).
3345
Let v = 10/1951 + 3594/821371. Let i = v - -13023/2947. What is the common denominator of i and 3/6 - (-118)/(-52)?
91
Suppose 0 = -3*i + 4*h + 305, -4*i = 2*h - 3*h - 398. Calculate the least common multiple of i and (-1 + 19)*(231/(-9))/(-7).
198
Let c = 5095 - 76468/15. What is the common denominator of c and ((-36)/160)/(45/132)?
150
Let r be (5 - 15/(-5)) + -6. Calculate the common denominator of 133/12 and (-54)/336*-9*(r - 6).
84
Let w(i) = -76*i**2 + 1530*i - 80. Calculate the lowest common multiple of w(20) and 75 + (-3 - (1 - 1)).
360
Let y = -9750109/14 - -696436. What is the common denominator of (-1)/42*86/4 and y?
84
Find the common denominator of 47/(-8)*(28/(-35))/2 and (-110)/(-217) + 0 - (-2)/(-4).
4340
Let a = -45 + 51. Let q be (a + -26)*(2252/(-10) - 0). Let d = q + -36079/8. Find the common denominator of -35/16 and d.
16
Let y be 36/2*204/(-18)*-22. Let b = -31361/7 + y. Find the common denominator of b and (8*4/12)/18.
189
What is the common denominator of 22185/(-56600) + 8/(256/12) and -107/30?
8490
Let p(l) = l + 5. Suppose 53*v = 52*v + r + 7, -2*r = v - 16. What is the least common multiple of p(-4) and v?
10
Suppose 0 = 4*k - t - 2, 3*k + 2*t = 4*t + 4. Suppose k = -39*p + 40*p. Calculate the least common multiple of (-2 + p)*27/(-18) and 6.
6
Let o = 1929/14 + -4757/35. Let s = -18/103 + -799/3090. Calculate the common denominator of o and s.
210
Let j = -321/7 + 29511/644. Let v = 562 + -3940/7. What is the common denominator of v and j?
644
Suppose -1120 = 5*l - h - 6203, 4049 = 4*l + 5*h. Calculate the least common multiple of 72 and l.
9144
Find the common denominator of (-45342)/(-46640) - ((-24)/(-40) + (-4)/(-10)) and 99/2120.
2120
Find the common denominator of -13 and 1/(-450)*((-1)/(-6))/((-1)/(-292)).
675
Find the common denominator of 4/(-7) - ((-2756)/9576 - 0) and 83/42.
2394
Let u be (1/2)/((-3)/(-174)). Let t = -27 + u. Suppose -26 = -r - 5*i, -t*r - 3*r - 2*i = -130. What is the smallest common multiple of r and 8?
104
Let j = -4710604477/3201 + 1471604. Calculate the common denominator of -123/10 and j.
32010
Let x = -1278439365595/2208 - -579003459. Let t = -2862/23 + x. Calculate the common denominator of -19/80 and t.
480
Let a = -317 - -305. Let b(j) = 2*j**3 + 25*j**2 + 4*j - 16. What is the lowest common multiple of 44 and b(a)?
880
Let j(k) = -684*k + 29. Let g be j(-8). Let n = g + -109909/20. Find the common denominator of n and -13/25.
100
Let k(j) = j**2 - 3*j + 2. Let m = -73 - -76. Let q be k(m). Suppose 4*w + 3*h = 11, 0 = -q*h - 2*h - 12. What is the lowest common multiple of w and 3?
15
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