Least Common Multiple (LCM) of 114 and 22
The least common multiple (LCM) of 114 and 22 is 1254.
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 22?
First, calculate the GCD of 114 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 22 = 5 remainder 4 |
| 2 | 22 ÷ 4 = 5 remainder 2 |
| 3 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 61 | 6283 |
| 80 and 63 | 5040 |
| 105 and 10 | 210 |
| 195 and 84 | 5460 |
| 116 and 100 | 2900 |