Least Common Multiple (LCM) of 123 and 172
The least common multiple (LCM) of 123 and 172 is 21156.
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 123 and 172?
First, calculate the GCD of 123 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 172 = 0 remainder 123 |
| 2 | 172 ÷ 123 = 1 remainder 49 |
| 3 | 123 ÷ 49 = 2 remainder 25 |
| 4 | 49 ÷ 25 = 1 remainder 24 |
| 5 | 25 ÷ 24 = 1 remainder 1 |
| 6 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 136 | 7480 |
| 157 and 17 | 2669 |
| 144 and 38 | 2736 |
| 96 and 119 | 11424 |
| 187 and 121 | 2057 |