Least Common Multiple (LCM) of 10 and 31
The least common multiple (LCM) of 10 and 31 is 310.
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 10 and 31?
First, calculate the GCD of 10 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 31 = 0 remainder 10 |
| 2 | 31 ÷ 10 = 3 remainder 1 |
| 3 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 37 | 5291 |
| 31 and 60 | 1860 |
| 160 and 135 | 4320 |
| 176 and 22 | 176 |
| 157 and 51 | 8007 |