Least Common Multiple (LCM) of 49 and 114
The least common multiple (LCM) of 49 and 114 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 49 and 114?
First, calculate the GCD of 49 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 114 = 0 remainder 49 |
| 2 | 114 ÷ 49 = 2 remainder 16 |
| 3 | 49 ÷ 16 = 3 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 122 | 16714 |
| 32 and 25 | 800 |
| 198 and 71 | 14058 |
| 165 and 66 | 330 |
| 48 and 23 | 1104 |