Least Common Multiple (LCM) of 55 and 140
The least common multiple (LCM) of 55 and 140 is 1540.
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 140?
First, calculate the GCD of 55 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 140 = 0 remainder 55 |
| 2 | 140 ÷ 55 = 2 remainder 30 |
| 3 | 55 ÷ 30 = 1 remainder 25 |
| 4 | 30 ÷ 25 = 1 remainder 5 |
| 5 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 178 | 24742 |
| 105 and 169 | 17745 |
| 44 and 46 | 1012 |
| 135 and 19 | 2565 |
| 76 and 35 | 2660 |