For example, you might need to find the least common multiple of 5 and 8. Since these are small numbers, it is appropriate to use this method.
For example, the first several multiples of 5 are 5, 10, 15, 20, 25, 30, 35, and 40.
For example, the first several multiples of 8 are 8, 16, 24, 32, 40, 48, 56, and 64.
For example, the lowest multiple 5 and 8 share is 40, so the least common multiple of 5 and 8 is 40.
For example, if you need to find the least common multiple of 20 and 84, you should use this method.
For example, 2×10=20{\displaystyle \mathbf {2} \times 10=20} and 2×5=10{\displaystyle \mathbf {2} \times \mathbf {5} =10}, so the prime factors of 20 are 2, 2, and 5. Rewriting as an equation, you get 20=2×2×5{\displaystyle 20=2\times 2\times 5}.
For example, 2×42=84{\displaystyle \mathbf {2} \times 42=84}, 7×6=42{\displaystyle \mathbf {7} \times 6=42}, and 3×2=6{\displaystyle \mathbf {3} \times \mathbf {2} =6}, so the prime factors of 84 are 2, 7, 3, and 2. Rewriting as an equation, you get 84=2×7×3×2{\displaystyle 84=2\times 7\times 3\times 2}.
For example, both numbers share a factor of 2, so write 2×{\displaystyle 2\times } and cross out a 2 in each number’s factorization equation. Each number also shares a second 2, so change the multiplication sentence to 2×2{\displaystyle 2\times 2} and cross out a second 2 in each factorization equation.
For example, in the equation 20=2×2×5{\displaystyle 20=2\times 2\times 5}, you crossed out both 2s, since these factors were shared with the other number. You have a factor of 5 left over, so add this to your multiplication sentence: 2×2×5{\displaystyle 2\times 2\times 5}. In the equation 84=2×7×3×2{\displaystyle 84=2\times 7\times 3\times 2}, you also crossed out both 2s. You have the factors 7 and 3 left over, so add these to your multiplication sentence: 2×2×5×7×3{\displaystyle 2\times 2\times 5\times 7\times 3}.
For example, 2×2×5×7×3=420{\displaystyle 2\times 2\times 5\times 7\times 3=420}. So, the least common multiple of 20 and 84 is 420.
For example, if you are trying to find the least common multiple of 18 and 30, write 18 in the top center of your grid, and 30 in the top right of your grid.
For example, since 18 and 30 are both even numbers, you know that that they both have a factor of 2. So write 2 in the top-left of the grid.
For example, 18÷2=9{\displaystyle 18\div 2=9}, so write 9 under 18 in the grid. 30÷2=15{\displaystyle 30\div 2=15}, so write 15 under 30 in the grid.
For example, 9 and 15 both have a factor of 3, so you would write 3 in the middle-left of the grid.
For example, 9÷3=3{\displaystyle 9\div 3=3}, so write 3 under 9 in the grid. 15÷3=5{\displaystyle 15\div 3=5}, so write 5 under 15 in the grid.
For example, since 2 and 3 are in the first column of the grid, and 3 and 5 are in the last row of the grid, you would write the sentence 2×3×3×5{\displaystyle 2\times 3\times 3\times 5}.
For example, 2×3×3×5=90{\displaystyle 2\times 3\times 3\times 5=90}. So, the least common multiple of 18 and 30 is 90.
For example, in the equation 15÷6=2remainder3{\displaystyle 15\div 6=2;{\text{remainder}};3}:15 is the dividend6 is the divisor2 is the quotient3 is the remainder.
For example, 15=6×2+3{\displaystyle 15=6\times 2+3}. The greatest common divisor is the largest divisor, or factor, that two numbers share. [14] X Research source In this method, you first find the greatest common divisor, and then use it to find the least common multiple.
For example, if you are trying to find the least common multiple of 210 and 45, you would calculate 210=45×4+30{\displaystyle 210=45\times 4+30}.
For example, 45=30×1+15{\displaystyle 45=30\times 1+15}.
For example, 30=15×2+0{\displaystyle 30=15\times 2+0}. Since the remainder is 0, you do not need to divide any further.
For example, since the last equation was 30=15×2+0{\displaystyle 30=15\times 2+0}, the last divisor was 15, and so 15 is the greatest common divisor of 210 and 45.
For example, 210×45=9450{\displaystyle 210\times 45=9450}. Dividing by the greatest common divisor, you get 945015=630{\displaystyle {\frac {9450}{15}}=630}. So, 630 is the least common multiple of 210 and 45.
