Least Common Multiple (LCM) of 31 and 38
The least common multiple (LCM) of 31 and 38 is 1178.
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 38?
First, calculate the GCD of 31 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 38 = 0 remainder 31 |
| 2 | 38 ÷ 31 = 1 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 77 | 924 |
| 39 and 143 | 429 |
| 43 and 149 | 6407 |
| 124 and 32 | 992 |
| 165 and 109 | 17985 |