Least Common Multiple (LCM) of 55 and 69
The least common multiple (LCM) of 55 and 69 is 3795.
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 69?
First, calculate the GCD of 55 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 69 = 0 remainder 55 |
| 2 | 69 ÷ 55 = 1 remainder 14 |
| 3 | 55 ÷ 14 = 3 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 128 | 384 |
| 165 and 50 | 1650 |
| 129 and 197 | 25413 |
| 196 and 112 | 784 |
| 182 and 65 | 910 |