Least Common Multiple (LCM) of 76 and 131
The least common multiple (LCM) of 76 and 131 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 76 and 131?
First, calculate the GCD of 76 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 131 = 0 remainder 76 |
| 2 | 131 ÷ 76 = 1 remainder 55 |
| 3 | 76 ÷ 55 = 1 remainder 21 |
| 4 | 55 ÷ 21 = 2 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 17 | 34 |
| 79 and 99 | 7821 |
| 172 and 49 | 8428 |
| 178 and 167 | 29726 |
| 45 and 110 | 990 |