Least Common Multiple (LCM) of 117 and 172
The least common multiple (LCM) of 117 and 172 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 117 and 172?
First, calculate the GCD of 117 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 172 = 0 remainder 117 |
| 2 | 172 ÷ 117 = 1 remainder 55 |
| 3 | 117 ÷ 55 = 2 remainder 7 |
| 4 | 55 ÷ 7 = 7 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 196 | 5880 |
| 74 and 106 | 3922 |
| 159 and 18 | 954 |
| 67 and 90 | 6030 |
| 134 and 61 | 8174 |