Least Common Multiple (LCM) of 140 and 149
The least common multiple (LCM) of 140 and 149 is 20860.
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 140 and 149?
First, calculate the GCD of 140 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 149 = 0 remainder 140 |
| 2 | 149 ÷ 140 = 1 remainder 9 |
| 3 | 140 ÷ 9 = 15 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 33 | 363 |
| 26 and 187 | 4862 |
| 189 and 99 | 2079 |
| 189 and 27 | 189 |
| 12 and 177 | 708 |