Least Common Multiple (LCM) of 55 and 145
The least common multiple (LCM) of 55 and 145 is 1595.
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 145?
First, calculate the GCD of 55 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 145 = 0 remainder 55 |
| 2 | 145 ÷ 55 = 2 remainder 35 |
| 3 | 55 ÷ 35 = 1 remainder 20 |
| 4 | 35 ÷ 20 = 1 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 200 | 39800 |
| 19 and 199 | 3781 |
| 65 and 95 | 1235 |
| 20 and 79 | 1580 |
| 178 and 143 | 25454 |