Least Common Multiple (LCM) of 120 and 31
The least common multiple (LCM) of 120 and 31 is 3720.
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 120 and 31?
First, calculate the GCD of 120 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 31 = 3 remainder 27 |
| 2 | 31 ÷ 27 = 1 remainder 4 |
| 3 | 27 ÷ 4 = 6 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 197 | 37036 |
| 73 and 15 | 1095 |
| 139 and 65 | 9035 |
| 186 and 43 | 7998 |
| 130 and 121 | 15730 |