Least Common Multiple (LCM) of 100 and 57
The least common multiple (LCM) of 100 and 57 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 100 and 57?
First, calculate the GCD of 100 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 57 = 1 remainder 43 |
| 2 | 57 ÷ 43 = 1 remainder 14 |
| 3 | 43 ÷ 14 = 3 remainder 1 |
| 4 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 17 | 187 |
| 144 and 108 | 432 |
| 73 and 40 | 2920 |
| 111 and 115 | 12765 |
| 200 and 35 | 1400 |