Least Common Multiple (LCM) of 55 and 49
The least common multiple (LCM) of 55 and 49 is 2695.
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 55 and 49?
First, calculate the GCD of 55 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 49 = 1 remainder 6 |
| 2 | 49 ÷ 6 = 8 remainder 1 |
| 3 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 45 | 630 |
| 10 and 61 | 610 |
| 178 and 85 | 15130 |
| 107 and 114 | 12198 |
| 142 and 59 | 8378 |