Least Common Multiple (LCM) of 57 and 100
The least common multiple (LCM) of 57 and 100 is 5700.
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 100?
First, calculate the GCD of 57 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 100 = 0 remainder 57 |
| 2 | 100 ÷ 57 = 1 remainder 43 |
| 3 | 57 ÷ 43 = 1 remainder 14 |
| 4 | 43 ÷ 14 = 3 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 189 | 11718 |
| 181 and 182 | 32942 |
| 189 and 193 | 36477 |
| 37 and 128 | 4736 |
| 54 and 111 | 1998 |