Least Common Multiple (LCM) of 31 and 119
The least common multiple (LCM) of 31 and 119 is 3689.
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 119?
First, calculate the GCD of 31 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 119 = 0 remainder 31 |
| 2 | 119 ÷ 31 = 3 remainder 26 |
| 3 | 31 ÷ 26 = 1 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 166 | 13612 |
| 199 and 29 | 5771 |
| 139 and 72 | 10008 |
| 56 and 64 | 448 |
| 37 and 49 | 1813 |