Least Common Multiple (LCM) of 31 and 67
The least common multiple (LCM) of 31 and 67 is 2077.
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 67?
First, calculate the GCD of 31 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 67 = 0 remainder 31 |
| 2 | 67 ÷ 31 = 2 remainder 5 |
| 3 | 31 ÷ 5 = 6 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 135 | 2295 |
| 17 and 13 | 221 |
| 15 and 67 | 1005 |
| 111 and 27 | 999 |
| 91 and 119 | 1547 |