Least Common Multiple (LCM) of 164 and 119
The least common multiple (LCM) of 164 and 119 is 19516.
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 164 and 119?
First, calculate the GCD of 164 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 119 = 1 remainder 45 |
| 2 | 119 ÷ 45 = 2 remainder 29 |
| 3 | 45 ÷ 29 = 1 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 175 | 25900 |
| 117 and 182 | 1638 |
| 79 and 159 | 12561 |
| 188 and 40 | 1880 |
| 105 and 79 | 8295 |