Least Common Multiple (LCM) of 116 and 165
The least common multiple (LCM) of 116 and 165 is 19140.
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 165?
First, calculate the GCD of 116 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 165 = 0 remainder 116 |
| 2 | 165 ÷ 116 = 1 remainder 49 |
| 3 | 116 ÷ 49 = 2 remainder 18 |
| 4 | 49 ÷ 18 = 2 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 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 |
|---|---|
| 111 and 135 | 4995 |
| 183 and 157 | 28731 |
| 175 and 172 | 30100 |
| 136 and 98 | 6664 |
| 173 and 75 | 12975 |