Least Common Multiple (LCM) of 138 and 143
The least common multiple (LCM) of 138 and 143 is 19734.
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 138 and 143?
First, calculate the GCD of 138 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 143 = 0 remainder 138 |
| 2 | 143 ÷ 138 = 1 remainder 5 |
| 3 | 138 ÷ 5 = 27 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 40 | 3560 |
| 191 and 111 | 21201 |
| 33 and 139 | 4587 |
| 97 and 146 | 14162 |
| 196 and 16 | 784 |