Least Common Multiple (LCM) of 57 and 187
The least common multiple (LCM) of 57 and 187 is 10659.
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 187?
First, calculate the GCD of 57 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 187 = 0 remainder 57 |
| 2 | 187 ÷ 57 = 3 remainder 16 |
| 3 | 57 ÷ 16 = 3 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 111 | 5106 |
| 54 and 80 | 2160 |
| 116 and 151 | 17516 |
| 141 and 148 | 20868 |
| 195 and 58 | 11310 |