Least Common Multiple (LCM) of 113 and 55
The least common multiple (LCM) of 113 and 55 is 6215.
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 113 and 55?
First, calculate the GCD of 113 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 55 = 2 remainder 3 |
| 2 | 55 ÷ 3 = 18 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 61 | 8357 |
| 44 and 70 | 1540 |
| 96 and 137 | 13152 |
| 185 and 149 | 27565 |
| 61 and 67 | 4087 |