Lowest common multiple

Find the lowest common multiple, and multiply each of the half-reactions by the appropriate factor to achieve this value. This is the key step, as the number of electrons lost MUST equal the number gained.)... 

To balance the total charge in the oxidation number, the half-reactions must be multiplied by the lowest common multiple of 6, which are 3 and 2 ... 

As (x) involves 6 electrons and (xi) involves 14, we have to find their lowest common multiple, which is 42. 

But our concern here is with the two-dimensional cases layered misfit structures, in which the lack of commensurability is between the intralayer periodicities of layers of two types, which alternate regularly through the structure. The layers may be simple or complex (i.e. composite groups of several, physically distinct layers). In most cases the two layer types compensate each other s valency and consequently alternate with strict regularity, forming double-layer or two-component layered structures. Both intralayer identity vectors of one layer set A) may differ fi-om those of the other layer set (B), so that each layer set has its own periodicities, and the vectors defining the net common to both (if it exists) are more or less complicated resultants (e.g. lowest common multiples) of these basic, intralayer vectors. In some cases the basic vectors are identical in one... 

To determine how to get a neutral compound, look for the lowest common multiple of the charges on the ions. The lowest common multiple of 3 and 2 is 6. Therefore, the formula should indicate six positive charges and six negative charges. 

One way to know what coefficient to use is to find a lowest common multiple. In this example, there were six hydrogen atoms in the products and two in the reactants. The lowest common multiple of 6 and 2 is 6, so a coefficient of 3 in the reactants balances the atoms. 

To write the formula of the compound, combine the smallest numbers of Ca and CF ions to give the charge sum equal to zero. In this case the lowest common multiple of the charges is 2 ... 

To find the lowest common multiple (LCM), multiply each charge by whatever number works to give the least common multiple. 

Tip lowest common multiple is easiest to use when the charge from one ion is used as the multiplier for the other ion.)... 

Consider the combination of weave of two single-layer fabrics. Let Mi and M2 be the matrices for two single-layer fabric sections. To unify the repeat size of the two layers, the lowest common multiple (1cm) is calculated based on the dimensions of these two matrices. Assume that di is the dimension of Mi and d2 that of M2. If cm di,d2) is equal to d (or d2), the dimension of M2 (or Mi) will be expanded to be of the same size of di (or d ). If cm di,d2) is larger than both di and c 2, then Ml and M2 will have to be expanded to the new dimension lcm(di, c/2) Let the enlarged matrix be ME. The elements of this matrix are assigned as follows ... 

The most challenging ion combination occurs when one ion has a charge of 3 and the other a charge of 2. The lowest common multiple is 6, so to obtain balance you must have two ions with a charge of 3 and three ions with a charge of 2. The next example illustrates this with both monatomic and polyatomic ions. 

The electrons that are lost in the oxidation halfreaction cire the Scime electrons that are gained in the reduction half-reaction, so the number of electrons lost and gained must be the same. But Step 6 shows a loss of two electrons and a gain of three. So you must adjust the numbers using appropriate multipliers for both half-reactions. In this case, you have to find the lowest common multiple of 2 and 3. It s 6, so multiply the first half-reaction by 3 and the second half-reaction by 2. 

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