Least Common Multiple (LCM) of 114 and 100
The least common multiple (LCM) of 114 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 114 and 100?
First, calculate the GCD of 114 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 100 = 1 remainder 14 |
| 2 | 100 ÷ 14 = 7 remainder 2 |
| 3 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 83 | 10126 |
| 175 and 57 | 9975 |
| 70 and 21 | 210 |
| 196 and 125 | 24500 |
| 149 and 101 | 15049 |