Least Common Multiple (LCM) of 83 and 178
The least common multiple (LCM) of 83 and 178 is 14774.
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 178?
First, calculate the GCD of 83 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 178 = 0 remainder 83 |
| 2 | 178 ÷ 83 = 2 remainder 12 |
| 3 | 83 ÷ 12 = 6 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 54 | 3456 |
| 119 and 52 | 6188 |
| 123 and 96 | 3936 |
| 185 and 22 | 4070 |
| 150 and 140 | 2100 |