Least Common Multiple (LCM) of 109 and 138
The least common multiple (LCM) of 109 and 138 is 15042.
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 109 and 138?
First, calculate the GCD of 109 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 138 = 0 remainder 109 |
| 2 | 138 ÷ 109 = 1 remainder 29 |
| 3 | 109 ÷ 29 = 3 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 40 | 480 |
| 38 and 44 | 836 |
| 180 and 122 | 10980 |
| 79 and 181 | 14299 |
| 108 and 173 | 18684 |