Least Common Multiple (LCM) of 31 and 179
The least common multiple (LCM) of 31 and 179 is 5549.
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 179?
First, calculate the GCD of 31 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 179 = 0 remainder 31 |
| 2 | 179 ÷ 31 = 5 remainder 24 |
| 3 | 31 ÷ 24 = 1 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 86 | 9202 |
| 91 and 39 | 273 |
| 138 and 129 | 5934 |
| 17 and 173 | 2941 |
| 27 and 65 | 1755 |