Least Common Multiple (LCM) of 127 and 157
The least common multiple (LCM) of 127 and 157 is 19939.
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 127 and 157?
First, calculate the GCD of 127 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 157 = 0 remainder 127 |
| 2 | 157 ÷ 127 = 1 remainder 30 |
| 3 | 127 ÷ 30 = 4 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 141 | 7896 |
| 129 and 186 | 7998 |
| 69 and 164 | 11316 |
| 88 and 65 | 5720 |
| 80 and 158 | 6320 |