Least Common Multiple (LCM) of 141 and 109
The least common multiple (LCM) of 141 and 109 is 15369.
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 141 and 109?
First, calculate the GCD of 141 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 141 ÷ 109 = 1 remainder 32 |
| 2 | 109 ÷ 32 = 3 remainder 13 |
| 3 | 32 ÷ 13 = 2 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 30 | 90 |
| 92 and 53 | 4876 |
| 171 and 45 | 855 |
| 112 and 112 | 112 |
| 21 and 24 | 168 |