Least Common Multiple (LCM) of 123 and 67
The least common multiple (LCM) of 123 and 67 is 8241.
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 67?
First, calculate the GCD of 123 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 67 = 1 remainder 56 |
| 2 | 67 ÷ 56 = 1 remainder 11 |
| 3 | 56 ÷ 11 = 5 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 190 | 12730 |
| 175 and 75 | 525 |
| 68 and 179 | 12172 |
| 133 and 55 | 7315 |
| 128 and 133 | 17024 |