Least Common Multiple (LCM) of 55 and 137
The least common multiple (LCM) of 55 and 137 is 7535.
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 137?
First, calculate the GCD of 55 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 137 = 0 remainder 55 |
| 2 | 137 ÷ 55 = 2 remainder 27 |
| 3 | 55 ÷ 27 = 2 remainder 1 |
| 4 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 112 | 1232 |
| 113 and 87 | 9831 |
| 80 and 199 | 15920 |
| 194 and 97 | 194 |
| 132 and 144 | 1584 |