Least Common Multiple (LCM) of 119 and 171
The least common multiple (LCM) of 119 and 171 is 20349.
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 171?
First, calculate the GCD of 119 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 171 = 0 remainder 119 |
| 2 | 171 ÷ 119 = 1 remainder 52 |
| 3 | 119 ÷ 52 = 2 remainder 15 |
| 4 | 52 ÷ 15 = 3 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 65 | 9620 |
| 117 and 130 | 1170 |
| 146 and 30 | 2190 |
| 78 and 16 | 624 |
| 81 and 22 | 1782 |