Least Common Multiple (LCM) of 119 and 164
The least common multiple (LCM) of 119 and 164 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 119 and 164?
First, calculate the GCD of 119 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 164 = 0 remainder 119 |
| 2 | 164 ÷ 119 = 1 remainder 45 |
| 3 | 119 ÷ 45 = 2 remainder 29 |
| 4 | 45 ÷ 29 = 1 remainder 16 |
| 5 | 29 ÷ 16 = 1 remainder 13 |
| 6 | 16 ÷ 13 = 1 remainder 3 |
| 7 | 13 ÷ 3 = 4 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 128 | 12672 |
| 74 and 79 | 5846 |
| 89 and 47 | 4183 |
| 127 and 86 | 10922 |
| 159 and 83 | 13197 |