Least Common Multiple (LCM) of 109 and 172
The least common multiple (LCM) of 109 and 172 is 18748.
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 109 and 172?
First, calculate the GCD of 109 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 172 = 0 remainder 109 |
| 2 | 172 ÷ 109 = 1 remainder 63 |
| 3 | 109 ÷ 63 = 1 remainder 46 |
| 4 | 63 ÷ 46 = 1 remainder 17 |
| 5 | 46 ÷ 17 = 2 remainder 12 |
| 6 | 17 ÷ 12 = 1 remainder 5 |
| 7 | 12 ÷ 5 = 2 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 45 | 6030 |
| 182 and 128 | 11648 |
| 194 and 178 | 17266 |
| 55 and 103 | 5665 |
| 10 and 102 | 510 |