Least Common Multiple (LCM) of 187 and 116
The least common multiple (LCM) of 187 and 116 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 187 and 116?
First, calculate the GCD of 187 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 116 = 1 remainder 71 |
| 2 | 116 ÷ 71 = 1 remainder 45 |
| 3 | 71 ÷ 45 = 1 remainder 26 |
| 4 | 45 ÷ 26 = 1 remainder 19 |
| 5 | 26 ÷ 19 = 1 remainder 7 |
| 6 | 19 ÷ 7 = 2 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 35 | 280 |
| 63 and 15 | 315 |
| 187 and 105 | 19635 |
| 118 and 17 | 2006 |
| 168 and 35 | 840 |