1170
Let j(m) = m**3 + 33*m**2 - 107*m + 42. Calculate the lowest common multiple of 312 and j(-36).
312
Suppose 2*j + 4*x + 13 = j, 2*j - 26 = 5*x. What is the common denominator of -49/50 and j + (-510)/175 + 0?
350
Let m = -598769225297/75784826810 - -418173/53218. Let u = m - -37/854. Let g = u - -416869/40020. What is the common denominator of -33/70 and g?
420
Calculate the least common multiple of ((-2)/10)/(75/(-375)) and 177.
177
Calculate the common denominator of ((-286)/(-24) - 2) + (-8)/(-12) and (-2 - -3) + 142/4.
12
Let n = 2 - 4. Let t = 136317/10 + -13644. What is the common denominator of t and n/(-7) + (-774)/112?
40
Let w(g) = g**3 - 4*g + 3. Let k be w(2). Suppose k*q - 6706 = q. Let u = q + -33653/10. What is the common denominator of u and 53/8?
40
Let k be (2/4 - 15/(-10)) + -1. What is the smallest common multiple of 288/72 - (1 + -59)/k and 4?
124
Suppose -3*x = 5*t - 161, -4*x - 23 = t - 2*t. Let o = 39 - t. What is the smallest common multiple of 10 + 0 + 0 + 0 and o?
40
Suppose -73*r = -69*r - 560. Calculate the smallest common multiple of 20 and r.
140
Let y(h) = h + 2. Let n(w) = -w**3 - 2*w**2 - 3*w - 2. Let b be n(-2). What is the smallest common multiple of y(b) and 22?
66
Let v(l) = 46*l**2 + 21*l - 18. Calculate the lowest common multiple of v(3) and 135.
2295
Find the common denominator of -11/3 and 5 - (5 + -5) - (-4074)/(-788).
1182
Let i(m) = m**3 - 5*m**2 - 2*m - 2. Let o(s) = -2*s**3 + 10*s**2 + 3*s + 5. Let k(t) = -13*i(t) - 6*o(t). What is the least common multiple of k(6) and 20?
40
Suppose -4*c = 4*c - 32. Let r(n) = 2*n - 6. What is the smallest common multiple of r(c) and ((-16)/10)/(4/(-50))?
20
Let h(q) = -6*q + 171. What is the smallest common multiple of 15 and h(24)?
135
Find the common denominator of -107/102 and (582/75)/(5/((-100)/(-16))).
510
Let m be (390/4)/((-4)/(-8)). Suppose -11*l - 41 + m = 0. Calculate the smallest common multiple of 38 and l.
266
Let x be 6/9*(-51)/(-2). Suppose -x*q = -23*q + 432. Calculate the least common multiple of 14 and q.
504
Let a = -1014 - -3011/3. Let h be (-1 + 89)/2*2. What is the common denominator of h*(2 - 6/4) and a?
3
Let g = 41 + 58. Suppose -2*j + g = 3*m, -4*j = -0*m + 2*m - 66. What is the least common multiple of m and 15?
165
Suppose -y - y - 106 = 0. Let v = 10 + y. Find the common denominator of v and -32/7.
7
Calculate the common denominator of (-21)/18*(-162)/78 and 18.
26
Let p be 4/(-10) + 484/10. What is the common denominator of (-50)/p*-1*-2 and (98/42)/(-7) - (-23)/(-4)?
12
Let u = -8425/6138 + 5/558. Calculate the common denominator of -23/14 and u.
154
Let t = -1567277/66 + 23746. What is the common denominator of -73/363 and t?
726
Suppose -29 + 27 = c. What is the least common multiple of 3 + 0 - (c + 1) and (-60)/(-1 + -2) + 0?
20
Let p = 50 - 71. Find the common denominator of (-6)/(-27) - (-37)/6 and p/(-4) - 5 - (-110)/(-32).
144
Let z = -80 - -138. What is the least common multiple of 12 and z?
348
Let b be 3/((-2)/8*3). Let o = b + 16. Calculate the least common multiple of o and 68/6 - (-4)/6.
12
Let m be ((-18)/36)/((-2)/808). Suppose 214 = 4*c - m. What is the least common multiple of (-2)/12 + c/48 and 12?
12
Let b(m) = -8*m - 15. Let n(v) = v**3 + 6*v**2 + v - 3. Let d be n(-6). Calculate the smallest common multiple of 2 and b(d).
114
Let y = -7/139 + -1653/3058. Let p = -11441/738 + 1/369. What is the common denominator of y and p?
22
Suppose -4*d + 2*l = -124, -112*l - 110 = -5*d - 117*l. Let x be (-414)/(-5) - (-1)/5. What is the common denominator of d and x/12 - (-3)/9?
4
Let g = 79 + -119. Let c = g + 37. What is the common denominator of ((-39)/(-18))/(c/15) and 19/30?
30
Find the common denominator of (3/6)/((-24)/24 - 194/(-190)) and 122/(-20) - 4/2.
20
Let x(a) = 8*a**2 + 1. Let t be x(1). Let w = -9 + t. Suppose -s - 4*n + 1 = w, -3*s + 1 = -2*n - 2. What is the least common multiple of s and 2?
2
Suppose 0 = -5*d - 3*q + 153, -d + 0*q = -4*q - 26. Calculate the lowest common multiple of 24 and d.
120
Suppose -h = 4*m - 121, -11*h = -6*h + 2*m - 515. What is the lowest common multiple of 4 and h?
404
What is the common denominator of (5 - 4) + 2/4 and (-642)/56 + (-5 - 132/(-28))?
4
Let v = -114 + 164. What is the lowest common multiple of v and (9/(-2))/(6/8*(-52)/390)?
450
Let q = 803/962 - 2/1443. Find the common denominator of q and 10 - (-1)/3*-1.
6
Suppose 0 = 5*x + 4*l - 21, -12 - 13 = -5*x - 5*l. Suppose 476 = 3*y + 167. Calculate the common denominator of 103/18 and (x/10)/(1/y).
90
Let t(x) = x**2 + 9*x - 1. Let g be t(-7). Let h = 15 + g. Suppose h = 3*i + 2*i - 110. Calculate the smallest common multiple of 14 and i.
154
Find the common denominator of 103/60 and 2/11 - (39005/5500 - 7).
300
Let u = 23864/3123 + -21/694. What is the common denominator of u and -15/22?
198
Let h(s) be the second derivative of -s**5/20 + s**4/3 + 7*s**3/6 + s**2/2 - 3*s. What is the lowest common multiple of h(5) and (4/6)/(2/18 - 0)?
66
Let t = 4774 - 2719. Let x = t - 20459/10. Calculate the common denominator of x and -139/6.
30
Let p = 63 - 50. Suppose p*i - 18*i = -10. Calculate the smallest common multiple of i and 8.
8
Let p(f) = f**3 + 5*f**2 - 19*f - 21. What is the smallest common multiple of p(-7) and 600?
4200
Let d = -13/40 + -523/360. Calculate the common denominator of (1/7)/(2/22) and d.
63
Suppose 11*h - 38 = -16. Let d(z) = -z - 8. Let s(m) = -2*m**2 + 5*m + 3. Let g be s(4). What is the least common multiple of h and d(g)?
2
Suppose 0 = -c - 2*u - 2*u - 32, -5*c - 224 = 4*u. Suppose 785 = 18*z + 29. What is the smallest common multiple of 20 and c/(-28)*z/4?
180
Let n(q) = 6*q**2 + 4*q + 2. Let h = 9 - 4. Suppose 3*c + 11 = m, -3*c = m + m + h. What is the smallest common multiple of m and n(-2)?
18
What is the common denominator of 97/114 and 2 + 1 - 390/81?
1026
Suppose 6*i - 119 - 49 = 0. What is the smallest common multiple of 228 and i?
1596
Let o(i) = i**3 - 15*i**2 - i + 20. Let n be o(15). Let g be 144/(-15) + (-2)/n. Calculate the smallest common multiple of 4 and -3*(-5)/g*-2.
12
Calculate the common denominator of 1 - 69/140 - (-34)/(-85) and 13/44.
308
Let v be 87/(-2 - (-69)/12). Let j = 63/5 - v. Calculate the common denominator of (10/(-15))/((-12)/429) and j.
30
Find the common denominator of (1 - 220/12) + 11 + -6 and -17/150.
150
Suppose -x = 3*f - 82, -f - 2*x + 34 = -5*x. Let d = f - 21. What is the least common multiple of 4 and d?
28
Let y = -86833/87648 - 18/913. Find the common denominator of -137/24 and y.
96
Suppose 20 = -4*o + 8. Find the common denominator of -47/8 and 4*-1 + o + 3237/432.
144
Let v(p) = 2*p + 2. Let q(d) = -d. Let r(n) = 2*q(n) - 2*v(n). Suppose 0*l + 40 = 5*l. Calculate the least common multiple of l and r(-4).
40
Let g = -27907/8 + 3484. Let u = -25 - -29. Calculate the common denominator of ((-4)/u)/(732/(-236) - -3) and g.
24
Find the common denominator of -1/42 and ((-5)/(-2))/5*536/(-56).
42
What is the least common multiple of -7 - (-5445)/63 - 4/(-7) and 80?
80
Let j(s) = s**2 - 22*s - 3. Let a be j(22). Calculate the common denominator of ((-5)/(-50))/(a/(-6)) and -95/8.
40
Let f = 10/753 - -22480/8283. Calculate the common denominator of f and ((-3)/(-2))/(117/141).
286
Let t be (-9)/(-3)*-1 - 42. Let o be 20 - 9/(t/20). Suppose -o = -3*n - 81. Find the common denominator of n and -17.
1
Let u(j) = -j**2 - 7*j - 8. Calculate the lowest common multiple of u(-3) and 12.
12
Let r be (-6)/10 + 3/5 + -1. Find the common denominator of 41/20 and (-450)/(-80) + (-3)/r.
40
What is the common denominator of 40/7 and (31 + -28)*10/(-34)?
119
Calculate the common denominator of 1/285 and (12 + (-2248)/192)*206/133.
1140
Suppose -5*v = 4*o - 197, -o - 8 = -v - 55. Calculate the smallest common multiple of 12 and o.
48
Find the common denominator of -121/20 and 1*141/(-36) - (-27)/162.
20
Calculate the smallest common multiple of 27*((-14)/6 - -3) and (16/10)/((-3)/(-15)).
72
Let p = 6038898717451/5230 - 1154665156. Let r = 107297 + -56116352/523. Let j = r + p. What is the common denominator of j and -99/4?
20
Let o = 102/5 + -23/20. Find the common denominator of -6 + (-6768)/(-704) + (-6)/8 and o.
44
Suppose -27 = 11*g - 8*g. Calculate the co