Least Common Multiple (LCM) of 120 and 39
The least common multiple (LCM) of 120 and 39 is 1560.
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 39?
First, calculate the GCD of 120 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 39 = 3 remainder 3 |
| 2 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 55 | 8745 |
| 90 and 18 | 90 |
| 126 and 178 | 11214 |
| 162 and 180 | 1620 |
| 70 and 54 | 1890 |