Least Common Multiple (LCM) of 120 and 106
The least common multiple (LCM) of 120 and 106 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 120 and 106?
First, calculate the GCD of 120 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 106 = 1 remainder 14 |
| 2 | 106 ÷ 14 = 7 remainder 8 |
| 3 | 14 ÷ 8 = 1 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 67 | 7504 |
| 189 and 177 | 11151 |
| 191 and 115 | 21965 |
| 139 and 32 | 4448 |
| 165 and 47 | 7755 |