Least Common Multiple (LCM) of 123 and 175
The least common multiple (LCM) of 123 and 175 is 21525.
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 175?
First, calculate the GCD of 123 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 175 = 0 remainder 123 |
| 2 | 175 ÷ 123 = 1 remainder 52 |
| 3 | 123 ÷ 52 = 2 remainder 19 |
| 4 | 52 ÷ 19 = 2 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 67 | 1541 |
| 85 and 185 | 3145 |
| 194 and 135 | 26190 |
| 55 and 116 | 6380 |
| 188 and 136 | 6392 |