Least Common Multiple (LCM) of 83 and 155
The least common multiple (LCM) of 83 and 155 is 12865.
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 155?
First, calculate the GCD of 83 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 155 = 0 remainder 83 |
| 2 | 155 ÷ 83 = 1 remainder 72 |
| 3 | 83 ÷ 72 = 1 remainder 11 |
| 4 | 72 ÷ 11 = 6 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 41 | 1312 |
| 76 and 86 | 3268 |
| 45 and 125 | 1125 |
| 20 and 112 | 560 |
| 159 and 117 | 6201 |