Least Common Multiple (LCM) of 31 and 59
The least common multiple (LCM) of 31 and 59 is 1829.
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 59?
First, calculate the GCD of 31 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 59 = 0 remainder 31 |
| 2 | 59 ÷ 31 = 1 remainder 28 |
| 3 | 31 ÷ 28 = 1 remainder 3 |
| 4 | 28 ÷ 3 = 9 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 35 | 6265 |
| 88 and 195 | 17160 |
| 91 and 33 | 3003 |
| 188 and 54 | 5076 |
| 40 and 199 | 7960 |