Least Common Multiple (LCM) of 172 and 119
The least common multiple (LCM) of 172 and 119 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 172 and 119?
First, calculate the GCD of 172 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 119 = 1 remainder 53 |
| 2 | 119 ÷ 53 = 2 remainder 13 |
| 3 | 53 ÷ 13 = 4 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 117 | 10413 |
| 14 and 183 | 2562 |
| 91 and 68 | 6188 |
| 107 and 122 | 13054 |
| 20 and 67 | 1340 |