Least Common Multiple (LCM) of 157 and 171
The least common multiple (LCM) of 157 and 171 is 26847.
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 171?
First, calculate the GCD of 157 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 171 = 0 remainder 157 |
| 2 | 171 ÷ 157 = 1 remainder 14 |
| 3 | 157 ÷ 14 = 11 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 84 | 1260 |
| 114 and 100 | 5700 |
| 60 and 173 | 10380 |
| 30 and 63 | 630 |
| 184 and 153 | 28152 |