Least Common Multiple (LCM) of 119 and 172
The least common multiple (LCM) of 119 and 172 is 20468.
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 172?
First, calculate the GCD of 119 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 172 = 0 remainder 119 |
| 2 | 172 ÷ 119 = 1 remainder 53 |
| 3 | 119 ÷ 53 = 2 remainder 13 |
| 4 | 53 ÷ 13 = 4 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 102 | 19482 |
| 23 and 23 | 23 |
| 74 and 115 | 8510 |
| 157 and 34 | 5338 |
| 22 and 146 | 1606 |