Least Common Multiple (LCM) of 57 and 155
The least common multiple (LCM) of 57 and 155 is 8835.
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 57 and 155?
First, calculate the GCD of 57 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 155 = 0 remainder 57 |
| 2 | 155 ÷ 57 = 2 remainder 41 |
| 3 | 57 ÷ 41 = 1 remainder 16 |
| 4 | 41 ÷ 16 = 2 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 152 | 1064 |
| 126 and 32 | 2016 |
| 129 and 41 | 5289 |
| 82 and 100 | 4100 |
| 43 and 93 | 3999 |