Least Common Multiple (LCM) of 49 and 108
The least common multiple (LCM) of 49 and 108 is 5292.
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 108?
First, calculate the GCD of 49 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 108 = 0 remainder 49 |
| 2 | 108 ÷ 49 = 2 remainder 10 |
| 3 | 49 ÷ 10 = 4 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 90 | 6120 |
| 187 and 112 | 20944 |
| 27 and 171 | 513 |
| 82 and 129 | 10578 |
| 176 and 58 | 5104 |