Least Common Multiple (LCM) of 107 and 157
The least common multiple (LCM) of 107 and 157 is 16799.
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 107 and 157?
First, calculate the GCD of 107 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 157 = 0 remainder 107 |
| 2 | 157 ÷ 107 = 1 remainder 50 |
| 3 | 107 ÷ 50 = 2 remainder 7 |
| 4 | 50 ÷ 7 = 7 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 162 | 8100 |
| 157 and 181 | 28417 |
| 67 and 25 | 1675 |
| 198 and 116 | 11484 |
| 101 and 119 | 12019 |