Least Common Multiple (LCM) of 157 and 83
The least common multiple (LCM) of 157 and 83 is 13031.
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 83?
First, calculate the GCD of 157 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 83 = 1 remainder 74 |
| 2 | 83 ÷ 74 = 1 remainder 9 |
| 3 | 74 ÷ 9 = 8 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 110 | 15290 |
| 106 and 12 | 636 |
| 148 and 41 | 6068 |
| 153 and 59 | 9027 |
| 183 and 151 | 27633 |