Least Common Multiple (LCM) of 31 and 88
The least common multiple (LCM) of 31 and 88 is 2728.
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 88?
First, calculate the GCD of 31 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 88 = 0 remainder 31 |
| 2 | 88 ÷ 31 = 2 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 |
|---|---|
| 108 and 147 | 5292 |
| 186 and 30 | 930 |
| 136 and 165 | 22440 |
| 149 and 89 | 13261 |
| 172 and 76 | 3268 |