Least Common Multiple (LCM) of 106 and 120
The least common multiple (LCM) of 106 and 120 is 6360.
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 120?
First, calculate the GCD of 106 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 120 = 0 remainder 106 |
| 2 | 120 ÷ 106 = 1 remainder 14 |
| 3 | 106 ÷ 14 = 7 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 67 | 8777 |
| 100 and 45 | 900 |
| 29 and 84 | 2436 |
| 192 and 54 | 1728 |
| 93 and 188 | 17484 |