Least Common Multiple (LCM) of 172 and 109
The least common multiple (LCM) of 172 and 109 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 172 and 109?
First, calculate the GCD of 172 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 109 = 1 remainder 63 |
| 2 | 109 ÷ 63 = 1 remainder 46 |
| 3 | 63 ÷ 46 = 1 remainder 17 |
| 4 | 46 ÷ 17 = 2 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 53 | 9487 |
| 153 and 89 | 13617 |
| 56 and 57 | 3192 |
| 144 and 48 | 144 |
| 169 and 120 | 20280 |