Least Common Multiple (LCM) of 108 and 121
The least common multiple (LCM) of 108 and 121 is 13068.
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 108 and 121?
First, calculate the GCD of 108 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 121 = 0 remainder 108 |
| 2 | 121 ÷ 108 = 1 remainder 13 |
| 3 | 108 ÷ 13 = 8 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 195 | 31980 |
| 45 and 126 | 630 |
| 80 and 139 | 11120 |
| 77 and 75 | 5775 |
| 159 and 13 | 2067 |