Least Common Multiple (LCM) of 120 and 109
The least common multiple (LCM) of 120 and 109 is 13080.
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 109?
First, calculate the GCD of 120 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 109 = 1 remainder 11 |
| 2 | 109 ÷ 11 = 9 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 113 | 16272 |
| 54 and 162 | 162 |
| 167 and 158 | 26386 |
| 112 and 193 | 21616 |
| 163 and 181 | 29503 |