Least Common Multiple (LCM) of 107 and 141
The least common multiple (LCM) of 107 and 141 is 15087.
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 107 and 141?
First, calculate the GCD of 107 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 141 = 0 remainder 107 |
| 2 | 141 ÷ 107 = 1 remainder 34 |
| 3 | 107 ÷ 34 = 3 remainder 5 |
| 4 | 34 ÷ 5 = 6 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 40 | 720 |
| 192 and 124 | 5952 |
| 21 and 190 | 3990 |
| 33 and 198 | 198 |
| 70 and 120 | 840 |