Least Common Multiple (LCM) of 106 and 119
The least common multiple (LCM) of 106 and 119 is 12614.
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 106 and 119?
First, calculate the GCD of 106 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 119 = 0 remainder 106 |
| 2 | 119 ÷ 106 = 1 remainder 13 |
| 3 | 106 ÷ 13 = 8 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 21 | 273 |
| 200 and 112 | 2800 |
| 124 and 188 | 5828 |
| 74 and 20 | 740 |
| 116 and 83 | 9628 |