Least Common Multiple (LCM) of 84 and 106
The least common multiple (LCM) of 84 and 106 is 4452.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 84 and 106?
First, calculate the GCD of 84 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 106 = 0 remainder 84 |
| 2 | 106 ÷ 84 = 1 remainder 22 |
| 3 | 84 ÷ 22 = 3 remainder 18 |
| 4 | 22 ÷ 18 = 1 remainder 4 |
| 5 | 18 ÷ 4 = 4 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 72 | 792 |
| 64 and 183 | 11712 |
| 162 and 200 | 16200 |
| 99 and 59 | 5841 |
| 194 and 87 | 16878 |