Least Common Multiple (LCM) of 140 and 167
The least common multiple (LCM) of 140 and 167 is 23380.
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 167?
First, calculate the GCD of 140 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 167 = 0 remainder 140 |
| 2 | 167 ÷ 140 = 1 remainder 27 |
| 3 | 140 ÷ 27 = 5 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 175 | 25200 |
| 120 and 41 | 4920 |
| 58 and 60 | 1740 |
| 193 and 80 | 15440 |
| 179 and 87 | 15573 |