Least Common Multiple (LCM) of 140 and 31
The least common multiple (LCM) of 140 and 31 is 4340.
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 140 and 31?
First, calculate the GCD of 140 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 31 = 4 remainder 16 |
| 2 | 31 ÷ 16 = 1 remainder 15 |
| 3 | 16 ÷ 15 = 1 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 14 | 826 |
| 152 and 110 | 8360 |
| 172 and 41 | 7052 |
| 156 and 101 | 15756 |
| 187 and 177 | 33099 |