Least Common Multiple (LCM) of 119 and 165
The least common multiple (LCM) of 119 and 165 is 19635.
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 119 and 165?
First, calculate the GCD of 119 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 165 = 0 remainder 119 |
| 2 | 165 ÷ 119 = 1 remainder 46 |
| 3 | 119 ÷ 46 = 2 remainder 27 |
| 4 | 46 ÷ 27 = 1 remainder 19 |
| 5 | 27 ÷ 19 = 1 remainder 8 |
| 6 | 19 ÷ 8 = 2 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 136 | 25704 |
| 96 and 136 | 1632 |
| 64 and 79 | 5056 |
| 102 and 162 | 2754 |
| 20 and 146 | 1460 |