Least Common Multiple (LCM) of 172 and 117
The least common multiple (LCM) of 172 and 117 is 20124.
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 117?
First, calculate the GCD of 172 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 117 = 1 remainder 55 |
| 2 | 117 ÷ 55 = 2 remainder 7 |
| 3 | 55 ÷ 7 = 7 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 73 | 4307 |
| 196 and 162 | 15876 |
| 117 and 23 | 2691 |
| 191 and 60 | 11460 |
| 69 and 44 | 3036 |