Least Common Multiple (LCM) of 108 and 172
The least common multiple (LCM) of 108 and 172 is 4644.
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 108 and 172?
First, calculate the GCD of 108 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 172 = 0 remainder 108 |
| 2 | 172 ÷ 108 = 1 remainder 64 |
| 3 | 108 ÷ 64 = 1 remainder 44 |
| 4 | 64 ÷ 44 = 1 remainder 20 |
| 5 | 44 ÷ 20 = 2 remainder 4 |
| 6 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 197 | 8471 |
| 162 and 97 | 15714 |
| 152 and 107 | 16264 |
| 150 and 142 | 10650 |
| 30 and 62 | 930 |