Least Common Multiple (LCM) of 109 and 143
The least common multiple (LCM) of 109 and 143 is 15587.
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 143?
First, calculate the GCD of 109 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 143 = 0 remainder 109 |
| 2 | 143 ÷ 109 = 1 remainder 34 |
| 3 | 109 ÷ 34 = 3 remainder 7 |
| 4 | 34 ÷ 7 = 4 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 70 | 4970 |
| 34 and 64 | 1088 |
| 157 and 24 | 3768 |
| 27 and 11 | 297 |
| 67 and 150 | 10050 |