Least Common Multiple (LCM) of 140 and 178
The least common multiple (LCM) of 140 and 178 is 12460.
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 178?
First, calculate the GCD of 140 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 178 = 0 remainder 140 |
| 2 | 178 ÷ 140 = 1 remainder 38 |
| 3 | 140 ÷ 38 = 3 remainder 26 |
| 4 | 38 ÷ 26 = 1 remainder 12 |
| 5 | 26 ÷ 12 = 2 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 35 | 105 |
| 159 and 59 | 9381 |
| 52 and 103 | 5356 |
| 166 and 144 | 11952 |
| 14 and 184 | 1288 |