Least Common Multiple (LCM) of 120 and 131
The least common multiple (LCM) of 120 and 131 is 15720.
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 131?
First, calculate the GCD of 120 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 131 = 0 remainder 120 |
| 2 | 131 ÷ 120 = 1 remainder 11 |
| 3 | 120 ÷ 11 = 10 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 24 | 1992 |
| 119 and 133 | 2261 |
| 128 and 104 | 1664 |
| 161 and 45 | 7245 |
| 148 and 105 | 15540 |