diff --git a/src/integer.h b/src/integer.h
index b8a78feb5a..1c6c5ca279 100644
--- a/src/integer.h
+++ b/src/integer.h
@@ -326,6 +326,15 @@ extern Obj RemInt( Obj opL, Obj opR );
 extern Obj GcdInt( Obj opL, Obj opR );
 
 
+/****************************************************************************
+**
+*F  LcmInt( <opL>, <opR> )  . . . . . . .  lcm of two integers
+**
+**  'LcmInt' returns the lcm of the two integers <opL> and <opR>.
+*/
+extern Obj LcmInt( Obj opL, Obj opR );
+
+
 /****************************************************************************
 **
 *F  AInvInt( <op> ) . . . . . . . . . . . . .  additive inverse of an integer
diff --git a/src/permutat.c b/src/permutat.c
index 79d61623e4..53270a0602 100644
--- a/src/permutat.c
+++ b/src/permutat.c
@@ -2707,7 +2707,6 @@ Obj             FuncOrderPerm (
     UInt2 *             ptKnown2;       /* pointer to temporary bag        */
     UInt4 *             ptKnown4;       /* pointer to temporary bag        */
     UInt                len;            /* length of one cycle             */
-    UInt                gcd, s, t;      /* gcd( len, ord ), temporaries    */
     UInt                p, q;           /* loop variables                  */
 
     /* check arguments and extract permutation                             */
@@ -2747,13 +2746,11 @@ Obj             FuncOrderPerm (
                     len++;  ptKnown2[q] = 1;
                 }
 
-                /* compute the gcd with the previously order ord           */
-                /* Note that since len is single precision, ord % len is to*/
-                gcd = len;  s = INT_INTOBJ( ModInt( ord, INTOBJ_INT(len) ) );
-                while ( s != 0 ) {
-                    t = s;  s = gcd % s;  gcd = t;
-                }
-                ord = ProdInt( ord, INTOBJ_INT( len / gcd ) );
+                ord = LcmInt( ord, INTOBJ_INT( len ) );
+
+                // update bag pointers, in case a garbage collection happened
+                ptPerm2  = CONST_ADDR_PERM2(perm);
+                ptKnown2 = ADDR_PERM2(TmpPerm);
 
             }
 
@@ -2787,13 +2784,11 @@ Obj             FuncOrderPerm (
                     len++;  ptKnown4[q] = 1;
                 }
 
-                /* compute the gcd with the previously order ord           */
-                /* Note that since len is single precision, ord % len is to*/
-                gcd = len;  s = INT_INTOBJ( ModInt( ord, INTOBJ_INT(len) ) );
-                while ( s != 0 ) {
-                    t = s;  s = gcd % s;  gcd = t;
-                }
-                ord = ProdInt( ord, INTOBJ_INT( len / gcd ) );
+                ord = LcmInt( ord, INTOBJ_INT( len ) );
+
+                // update bag pointers, in case a garbage collection happened
+                ptPerm4  = CONST_ADDR_PERM4(perm);
+                ptKnown4 = ADDR_PERM4(TmpPerm);
 
             }
 
diff --git a/src/pperm.c b/src/pperm.c
index f03fc61ba4..8c7dd1b18f 100644
--- a/src/pperm.c
+++ b/src/pperm.c
@@ -617,7 +617,7 @@ Obj FuncPREIMAGE_PPERM_INT(Obj self, Obj f, Obj pt)
 // the least m, r such that f^m=f^m+r
 Obj FuncINDEX_PERIOD_PPERM(Obj self, Obj f)
 {
-    UInt    i, len, j, pow, gcd, rank, k, deg, n;
+    UInt    i, len, j, pow, rank, k, deg, n;
     UInt2 * ptf2;
     UInt4 * ptseen, *ptf4;
     Obj     dom, img, ord, out;
@@ -670,14 +670,9 @@ Obj FuncINDEX_PERIOD_PPERM(Obj self, Obj f)
                     len++;
                     ptseen[k - 1] = 0;
                 }
-                gcd = len;
-                j = INT_INTOBJ(ModInt(ord, INTOBJ_INT(len)));
-                while (j != 0) {
-                    k = j;
-                    j = gcd % j;
-                    gcd = k;
-                }
-                ord = ProdInt(ord, INTOBJ_INT(len / gcd));
+                ord = LcmInt(ord, INTOBJ_INT(len));
+                // update ptseen, in case a garbage collection happened
+                ptseen = (UInt4 *)(ADDR_OBJ(TmpPPerm));
             }
         }
     }
@@ -712,14 +707,9 @@ Obj FuncINDEX_PERIOD_PPERM(Obj self, Obj f)
                     len++;
                     ptseen[k - 1] = 0;
                 }
-                gcd = len;
-                j = INT_INTOBJ(ModInt(ord, INTOBJ_INT(len)));
-                while (j != 0) {
-                    k = j;
-                    j = gcd % j;
-                    gcd = k;
-                }
-                ord = ProdInt(ord, INTOBJ_INT(len / gcd));
+                ord = LcmInt(ord, INTOBJ_INT(len));
+                // update ptseen, in case a garbage collection happened
+                ptseen = (UInt4 *)(ADDR_OBJ(TmpPPerm));
             }
         }
     }
diff --git a/src/trans.c b/src/trans.c
index 43cff15f0f..66a4fca325 100644
--- a/src/trans.c
+++ b/src/trans.c
@@ -1406,7 +1406,7 @@ Obj FuncIndexPeriodOfTransformation(Obj self, Obj f)
     UInt4 * seen;
     UInt    deg, i, pt, dist, pow, len, last_pt;
     Obj     ord, out;
-    Int     s, t, gcd, cyc;
+    Int     cyc;
 
     if (!IS_TRANS(f)) {
         ErrorQuit("IndexPeriodOfTransformation: the argument must be a "
@@ -1464,18 +1464,14 @@ Obj FuncIndexPeriodOfTransformation(Obj self, Obj f)
                         seen[pt] = 1;
                     }
 
-                    // compute the gcd of the cycle length with the previous
-                    // order ord
-                    gcd = cyc;
-                    s = INT_INTOBJ(ModInt(ord, INTOBJ_INT(cyc)));
-                    while (s != 0) {
-                        t = s;
-                        s = gcd % s;
-                        gcd = t;
-                    }
-                    ord = ProdInt(ord, INTOBJ_INT(cyc / gcd));
-                    dist = len - cyc + 1;
+                    ord = LcmInt(ord, INTOBJ_INT(cyc));
+
                     // the distance of i from the cycle in its component + 1
+                    dist = len - cyc + 1;
+
+                    // update bag pointers, in case a garbage collection happened
+                    ptf2 = CONST_ADDR_TRANS2(f);
+                    seen = ADDR_TRANS4(TmpTrans);
                 }
                 if (dist > pow) {
                     pow = dist;
@@ -1513,18 +1509,14 @@ Obj FuncIndexPeriodOfTransformation(Obj self, Obj f)
                         seen[pt] = 1;
                     }
 
-                    // compute the gcd of the cycle length with the previous
-                    // order ord
-                    gcd = cyc;
-                    s = INT_INTOBJ(ModInt(ord, INTOBJ_INT(cyc)));
-                    while (s != 0) {
-                        t = s;
-                        s = gcd % s;
-                        gcd = t;
-                    }
-                    ord = ProdInt(ord, INTOBJ_INT(cyc / gcd));
-                    dist = len - cyc + 1;
+                    ord = LcmInt(ord, INTOBJ_INT(cyc));
+
                     // the distance of i from the cycle in its component + 1
+                    dist = len - cyc + 1;
+
+                    // update bag pointers, in case a garbage collection happened
+                    ptf4 = CONST_ADDR_TRANS4(f);
+                    seen = ADDR_TRANS4(TmpTrans);
                 }
                 if (dist > pow) {
                     pow = dist;