Least Common Multiple (LCM) of 108 and 143
The least common multiple (LCM) of 108 and 143 is 15444.
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 143?
First, calculate the GCD of 108 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 143 = 0 remainder 108 |
| 2 | 143 ÷ 108 = 1 remainder 35 |
| 3 | 108 ÷ 35 = 3 remainder 3 |
| 4 | 35 ÷ 3 = 11 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 150 | 9150 |
| 87 and 71 | 6177 |
| 180 and 51 | 3060 |
| 88 and 170 | 7480 |
| 106 and 121 | 12826 |