Least Common Multiple (LCM) of 157 and 82
The least common multiple (LCM) of 157 and 82 is 12874.
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 157 and 82?
First, calculate the GCD of 157 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 82 = 1 remainder 75 |
| 2 | 82 ÷ 75 = 1 remainder 7 |
| 3 | 75 ÷ 7 = 10 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 79 | 9164 |
| 55 and 180 | 1980 |
| 96 and 182 | 8736 |
| 42 and 112 | 336 |
| 102 and 89 | 9078 |