Least Common Multiple (LCM) of 31 and 55
The least common multiple (LCM) of 31 and 55 is 1705.
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 55?
First, calculate the GCD of 31 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 55 = 0 remainder 31 |
| 2 | 55 ÷ 31 = 1 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 |
|---|---|
| 59 and 97 | 5723 |
| 84 and 111 | 3108 |
| 27 and 66 | 594 |
| 57 and 38 | 114 |
| 140 and 112 | 560 |