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 |
|---|---|
| 112 and 148 | 4144 |
| 103 and 63 | 6489 |
| 155 and 64 | 9920 |
| 115 and 84 | 9660 |
| 195 and 144 | 9360 |