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 |
|---|---|
| 112 and 49 | 784 |
| 140 and 168 | 840 |
| 191 and 161 | 30751 |
| 23 and 64 | 1472 |
| 38 and 196 | 3724 |