Least Common Multiple (LCM) of 131 and 178
The least common multiple (LCM) of 131 and 178 is 23318.
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 178?
First, calculate the GCD of 131 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 178 = 0 remainder 131 |
| 2 | 178 ÷ 131 = 1 remainder 47 |
| 3 | 131 ÷ 47 = 2 remainder 37 |
| 4 | 47 ÷ 37 = 1 remainder 10 |
| 5 | 37 ÷ 10 = 3 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 65 | 1170 |
| 160 and 153 | 24480 |
| 48 and 108 | 432 |
| 84 and 14 | 84 |
| 96 and 131 | 12576 |