Least Common Multiple (LCM) of 116 and 187
The least common multiple (LCM) of 116 and 187 is 21692.
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 116 and 187?
First, calculate the GCD of 116 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 187 = 0 remainder 116 |
| 2 | 187 ÷ 116 = 1 remainder 71 |
| 3 | 116 ÷ 71 = 1 remainder 45 |
| 4 | 71 ÷ 45 = 1 remainder 26 |
| 5 | 45 ÷ 26 = 1 remainder 19 |
| 6 | 26 ÷ 19 = 1 remainder 7 |
| 7 | 19 ÷ 7 = 2 remainder 5 |
| 8 | 7 ÷ 5 = 1 remainder 2 |
| 9 | 5 ÷ 2 = 2 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 69 | 2622 |
| 37 and 131 | 4847 |
| 125 and 122 | 15250 |
| 29 and 17 | 493 |
| 107 and 63 | 6741 |