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 |
|---|---|
| 54 and 140 | 3780 |
| 109 and 106 | 11554 |
| 131 and 34 | 4454 |
| 199 and 180 | 35820 |
| 96 and 31 | 2976 |