Least Common Multiple (LCM) of 114 and 49
The least common multiple (LCM) of 114 and 49 is 5586.
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 49?
First, calculate the GCD of 114 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 49 = 2 remainder 16 |
| 2 | 49 ÷ 16 = 3 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 76 | 1292 |
| 173 and 119 | 20587 |
| 125 and 184 | 23000 |
| 157 and 142 | 22294 |
| 42 and 20 | 420 |