Least Common Multiple (LCM) of 131 and 76
The least common multiple (LCM) of 131 and 76 is 9956.
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 131 and 76?
First, calculate the GCD of 131 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 76 = 1 remainder 55 |
| 2 | 76 ÷ 55 = 1 remainder 21 |
| 3 | 55 ÷ 21 = 2 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 136 | 21352 |
| 118 and 123 | 14514 |
| 56 and 188 | 2632 |
| 113 and 33 | 3729 |
| 13 and 20 | 260 |