Least Common Multiple (LCM) of 120 and 139
The least common multiple (LCM) of 120 and 139 is 16680.
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 139?
First, calculate the GCD of 120 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 139 = 0 remainder 120 |
| 2 | 139 ÷ 120 = 1 remainder 19 |
| 3 | 120 ÷ 19 = 6 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 178 | 5518 |
| 32 and 121 | 3872 |
| 106 and 132 | 6996 |
| 195 and 135 | 1755 |
| 105 and 50 | 1050 |