Least Common Multiple (LCM) of 108 and 157
The least common multiple (LCM) of 108 and 157 is 16956.
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 108 and 157?
First, calculate the GCD of 108 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 157 = 0 remainder 108 |
| 2 | 157 ÷ 108 = 1 remainder 49 |
| 3 | 108 ÷ 49 = 2 remainder 10 |
| 4 | 49 ÷ 10 = 4 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 106 | 4558 |
| 59 and 13 | 767 |
| 61 and 138 | 8418 |
| 190 and 107 | 20330 |
| 89 and 127 | 11303 |