Least Common Multiple (LCM) of 83 and 154
The least common multiple (LCM) of 83 and 154 is 12782.
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 83 and 154?
First, calculate the GCD of 83 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 154 = 0 remainder 83 |
| 2 | 154 ÷ 83 = 1 remainder 71 |
| 3 | 83 ÷ 71 = 1 remainder 12 |
| 4 | 71 ÷ 12 = 5 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 123 | 3690 |
| 139 and 120 | 16680 |
| 144 and 105 | 5040 |
| 54 and 63 | 378 |
| 25 and 29 | 725 |