Least Common Multiple (LCM) of 114 and 106
The least common multiple (LCM) of 114 and 106 is 6042.
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 114 and 106?
First, calculate the GCD of 114 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 106 = 1 remainder 8 |
| 2 | 106 ÷ 8 = 13 remainder 2 |
| 3 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 120 | 12120 |
| 111 and 14 | 1554 |
| 200 and 18 | 1800 |
| 121 and 21 | 2541 |
| 160 and 74 | 5920 |