Least Common Multiple (LCM) of 178 and 140
The least common multiple (LCM) of 178 and 140 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 178 and 140?
First, calculate the GCD of 178 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 140 = 1 remainder 38 |
| 2 | 140 ÷ 38 = 3 remainder 26 |
| 3 | 38 ÷ 26 = 1 remainder 12 |
| 4 | 26 ÷ 12 = 2 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 112 | 4368 |
| 85 and 73 | 6205 |
| 77 and 98 | 1078 |
| 197 and 127 | 25019 |
| 123 and 173 | 21279 |