Least Common Multiple (LCM) of 155 and 107
The least common multiple (LCM) of 155 and 107 is 16585.
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 155 and 107?
First, calculate the GCD of 155 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 107 = 1 remainder 48 |
| 2 | 107 ÷ 48 = 2 remainder 11 |
| 3 | 48 ÷ 11 = 4 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 91 | 16016 |
| 138 and 101 | 13938 |
| 138 and 137 | 18906 |
| 141 and 27 | 1269 |
| 36 and 164 | 1476 |