Least Common Multiple (LCM) of 31 and 178
The least common multiple (LCM) of 31 and 178 is 5518.
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 31 and 178?
First, calculate the GCD of 31 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 178 = 0 remainder 31 |
| 2 | 178 ÷ 31 = 5 remainder 23 |
| 3 | 31 ÷ 23 = 1 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 69 | 2346 |
| 139 and 189 | 26271 |
| 196 and 74 | 7252 |
| 159 and 112 | 17808 |
| 121 and 89 | 10769 |