Least Common Multiple (LCM) of 31 and 107
The least common multiple (LCM) of 31 and 107 is 3317.
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 107?
First, calculate the GCD of 31 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 107 = 0 remainder 31 |
| 2 | 107 ÷ 31 = 3 remainder 14 |
| 3 | 31 ÷ 14 = 2 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 167 | 10688 |
| 110 and 74 | 4070 |
| 108 and 160 | 4320 |
| 152 and 190 | 760 |
| 32 and 151 | 4832 |