Least Common Multiple (LCM) of 110 and 140
The least common multiple (LCM) of 110 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 110 and 140?
First, calculate the GCD of 110 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 140 = 0 remainder 110 |
| 2 | 140 ÷ 110 = 1 remainder 30 |
| 3 | 110 ÷ 30 = 3 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 101 | 7272 |
| 30 and 29 | 870 |
| 85 and 57 | 4845 |
| 77 and 18 | 1386 |
| 151 and 10 | 1510 |